Runs perfectly fine.

Considering the map is huge, it's covered in death-star architecture, how well does the map run? Is the surface entirely static meshes, etc? Will I need to sell a kidney in order to run it?

The Empire did underestimate the Rebellion, never the less, they would have succeeded in thwarting the Rebels' assault on the exhaust port had it not been for the timely intervention of a certain Correllian smuggler and his Wookie co-pilot (who, at that point, was not affiliated with the Rebel Alliance).

At that point, the Rebel's attack pattern had already been successfully analyzed and appropriate measures were taken to stop them (Tarkin, being the brilliant tactician he was, was already fully aware of it even before being "informed"). Had it not been for the son of the chosen one and his natural attunement to the force, it's a good bet Yavin IV would've been obliterated.

With the insane amount of jamming, counter jamming, and natural interference from the massive structure, successfully locking on to the exhaust port posed a major problem for the X-wings. Y-wings were the main attack fighters partly due to their pin-point precise targeting systems (they were able to lock on to the exhaust port without any problems). However, several fatal mistakes were made on their approach to the port which cost the 3 pilots of Gold Squadron their lives and almost completely botched the assault.

Many T.I.E. Fighters were launched to intercept the assaulting Rebel fighters (of which there were 30 total; 22 X-wings & 8 Y-wings) and almost all were shot down by T.I.E. Fighters (& Vader's T.I.E. Advanced x1 prototype) save for the 3 that survived and at least one (Porkins) that was shot down by Turbo Laser fire.

Naturally, due to severe budget and time limitations, ILM wasn't able to convey a more appropriate and more realistic Imperial counter attack. Would've been nice had they done it with the Special Editions. Then again, there were A LOT of things they should've done but didn't. lol

T.I.E. Bombers were in Imperial service during the time of ANH, and squadrons of them were stationed on the Death Star, but like it's been said, ship to ship combat is not part of their combat designation so they weren't deployed against the assaulting Rebel fighters. But they can be armed with a large assortment of warheads, including proton torpedoes.