1. It could. There's nothing inherently wrong with it. Either the solid axle ST/GT or the IRS GT-S could work fine. It's 200-300lbs heavier than the AE86, but it has a stronger chassis. Unfortunately the IRS on the GT-S is a rather primitive semi-trailing arm setup.
2. Not much. Convertibles bring the most, and you don't really want that. Watch out for rust, though. These rust pretty bad, if they've spent any time in the North or were neglected.
3. Not at all. They are very simple cars with plenty of space in the engine bay.
4. 22RT-E from the pickup is a solid motor that is a direct bolt in. With a little work, it can make some good power. The 3T-GTE (or the homologation 4T-GTE) was used in Japan, but it would be very difficult to find parts for it here. There was also the 18R-GE, but it probably wouldn't be worth the trouble of locating one. Some people have squeezed the 7M in it, but it's a tight fit. It's even tighter to try to squeeze a JZ motor in, but it's been done. Some have also swapped the 1UZ in it, but both the JZ and UZ require a fair bit of fabrication work.