If Republican air units are used on Interdiction, precisely when are the counters removed (and recycled)?
They are removed at the start of the next Republican turn.

Also, does air interdiction affect tracing supply as well,
No it doesn’t. Interdictors only affect movement.

Since supply is traced using leg movement points
. This comment dumbfounded me and I just didn’t want to say anything until I checked the rules as printed. Leg MPs were tested during the game development, but were dropped soon as this supply system simply made the historical rate of advance impossible. The use of hexes instead of MPs allows historical advances possible (but you’ll have to think twice where to put your HQs if you want to advance along the three roads/tracks leading west as was historically done... not easy, but perfectly possible). The old version of the rule must have remained there unnoticed for months while we playtested with the new and correct one (it’s absolutely amazing what one can miss when reading the same rule zillions of times).

Does the Start Line restrict either side's set up? Both the Republican and Nationalists forces have opportunities to set up on either side of the line.
Yes, it does. Italian-Nationalist units north/east of the line; Republican units south/west of the line.

Another Guadalajara question: In the Tank After Combat Table (i.e. where only one side has armor), presumably you only roll one die? (I don't think it's specified)
Just one die

Another (dumb) Guadalajara question: Presumably, the truck counters are markers and not actual units. That is, they can be removed from one unit (at the beginning of movement) and instantaneously be placed on another, regardless of its location on the map (presuming a truck counter could legally be placed there) rather than have to be moved to the new unit to be transported. Correct?
You were more or less correct. Clarification added to errata.

The real constriction is the Italian supply rules, which keep them from going too far afield. For instance, there is a very tempting alternate route to Masegoso but the Italians can't use it because they can't keep the units supplied. This is a very restrictive rule and does more to keep units tied to transportation lines than anything else.
The correct rule is less restrictive and allows your tempting alternate route... nevertheless you are right: transportation lines are VERY important in this game (as they should be in any wargame portraying a battle fought in muddy terrain and under terrific weather conditions).

We are getting ready to start Turn 5, which sees the arrival of significant Republican air power which, through Interdiction, should put real brake on the Italian advance, such as it is (by keeping the HQ's from moving very far and attacking them)
Not now... too late to make decisive damage to the Italian advance. A nuisance yes, a real brake no. Immediate reconstitution of HQs intends to prevent massive OOS condition due to HQ hunting. You found a hole here... Interdictors will be unable to attack HQs (they can interdict their advance, though).

We wondered a bit about the movement restrictions since, according to the notes (Pg 14), on March 9 (i.e. Turn 2) The Italians, "...reached Argecilla and taking Cogoloor, Masegoso and the bridge over the Tajufia." We wondered about this since, in the game, the only way the Italians can even reach these locales is if the Italians motorize some infantry (and they only have two trucks and can therefore motorized only two infantry units) and the Republicans move completely out of the way.
In turn 2 the Italians receive a lot of trucks so they can reach all those locations without problem (provided the correct set up, that is )

This led us to the real problem. Our Republicans have left the highway to Torijo completely open... not one unit defending it. because of the Brihuega rule, it is if the road is sealed off by a gigantic seismic fault that is uncrossable. Instead, the Republicans have sent every unit (save one or two sent north) to defend Brihuega
. No longer possible using the correct set up and supply rules. Unless you roll the worst dice in your life for 4-5 consecutive times Brihuega will be in your hand by the end of turn 2, before the Republicans can prevent it. Why then the seismic fault rule? Because a short series of fortunate die rolls may otherwise allow the Italians to win a sudden death victory in a couple of turns, completely killing the game. To prevent it I decided to add a design-for-effect rule that works better than you may think (always talking under the correct set up and supply rule): Brihuega falls during the second turn, so no real stop to the advance on Torija... why does it work to prevent a sudden death then? Because the trucks you need to make the phantom advance are the ones you need to take Brihuega before the Republicans arrive so the possibility of an unavoidable sudden death due to a gifted hand is gone. Besides, this rule makes the flow of the game much more historical than a simple hell on wheels advance along the main road. Brihuega is not a simple village out of the main road: it not only opens an alternate route to Torija, but also to Guadalajara (if you follow the road leading southwards you’ll soon find an exit to the west leading to Guadalajara); furthermore, an advance along that south leading route would lead you to put a mortal threat to Madrid as you would be in position to cut the Madrid-Valencia road, the only lifeline of the capital in that moment... but this would be a completely different game.

Now it appears that this tactic is as effective as it is gamey.
It was... although it will not be possible from now on... you’ll have to defend all axis of Italian advance effectively or you will be toast.

I think I'll restart my first game and see if by using the Optional rules if the IT can rush to the big "B" (as close as possible at least before the Republicans show up) That exploit movement for IT in the Optional Surprise rule will be important here....
And still more important... the rule is no longer optional and must be enforced in all games.

Also, you only start with two truck units, so whatever you shove down the road is going to be pretty weak.
Once the Republicans are in position to attack Brihuega the Italians are strong enough to fight there... in fact strong enough to push a little more.

And since trucks can't move off road they aren't going far on the first turn.
Indeed they are... the correct set up leaves several axis of advance lightly defended, as it really was.

Oh well Ill still give it the school try, but it does seem difficult for the Nationalists to gain any victory given that the Republicans can jam the way to Brihuega
I’d really appreciate your giving the school try under the new conditions... a completely different game now.

When placing an air marker for interdiction, if you place the marker on a motorized unit (on a road), may the marker attack that unit if it moves out of the hex? May it attack it if it doesn't move at all?
No and no... it can only attack units moving through the hex, not units moving from or stopping into the hex.

And while we are at it....Am I correct in assuming that there is no overrun in this game.....gracias!
No, you aren’t... overruns are perfectly possible as there are a lot of hexes costing 1 or 2 MPs. A clarification has been added to errata.

Reluctantly, I have decided to toss in my hand after Game Turn 6 and start over. This, despite the Italians losing exactly zero steps.
Because I played "naturally" (which is not synonymous with efficiently), there is simply no way that the Italians can take Brihuega with enough time (assuming they can even take it in the first place) to capture enough villages to gain anything resembling victory.
Regardless of other problems which have already been solved... are you sure you were playing aggressively enough? Zero steps in 6 turns just looks suspicious if you are trying to advance at any cost...

The "problem," of course, is the Brihuega rule that prohibits the Italians from advancing west of the 16xx hex row until they take the village.
No, not really... the problem was a mistaken set up and a stupid supply rule errata that prevented you from taking Brihuega as soon as you should.
But they can hole up in one or two key villages, which will make things tough for the Nationalists since they have little artillery and the defenders gain either double defense or a column shift. If the Nationalists mass their forces to attack these villages, they leave a lot of ground open.
No need to do so... just cut their supply.

In this game, there is no real surprise combats in the South, as most of the Republicans are set up to far in the rear to be attacked on the first turn (a nice defense in depth actually) and the Italians can never reach Brihuega before the end of the 3rd day. At which point International Brigade is already in Front of the village with several battalions, with the rest just behind.
No longer an issue

The other rule that bothers me is the rule that prevents the Nationalists from moving south of the river/line. At least the game notes explain why this is so, so we can understand the rationale behind it. But I fear that it falls afoul of the Law of Unintended Consequences. because the Republicans know the nationalists can't cross the river, they do not have to defend the crossings and, in fact, might be better off not doing so. That way, they tie down a Nationalist unit (and there are few enough of them, to begin with) without having to expend one themselves (because they might move north).
This is an intended effect. During the full battle the Spanish Nationalists problem was the scarce number of units they had, no matter how good they were. In fact, the reinforcements arriving in the last turns were hurriedly sent to the front as the units on the field were not enough to cover the river line when the Republicans advanced while keeping all the ground they had previously gained.

Can rail bridges be treated as regular bridges for movement purposes, i.e. can armor use a RR bridge to cross a river ?
Yes

I had a 10-1 attack into a minor village( I know, I shoulda overran). Do I use the 4-1 column or does it go to 3-1 due to the column shift for attacking a minor village ?
3-1... and yes you should overrun, if possible

When trucks are listed as reinforcements, must they enter with other reinforcements that turn or can they be used with units already on the map?
They can be used with any unit. Besides, units entering as reinforcements can enter the map loaded on trucks entering as reinforcements that same turn (in other words they don’t pay 2 MPs to load)