The Windows "fix" for the FX processor doesn't affect their gaming performance. What's important for games like Skyrim performance-per-core, and when AMD made the FX processors they focused on multithreaded performance, which is multiple cores working together on tasks that can use all threads, such as video encoding. Good processors, but if your goal is gaming you don't need to buy anything better than the FX-4170.
A 7770 will run Skyrim on high comfortably.
There's no way to know what will be sufficient for 5 years from now. Games could get worlds more demanding or they could move almost entirely to mobile platforms, keeping their hardware demands relatively the same. But an i5, 4gb of RAM, and an HD 7770 should be able to play any game coming out soon comfortably on high, maybe medium if it's really crazy.
1gb vs 2gb memory on a video card makes very little difference on a single HD monitor. My 6950 isn't bottlenecked at all by its 1gb. The reason cards like the HD 7850 come with 2gb instead of 1gb is for two reasons:
-Triple-monitor gaming with Eyefinity and such require more than 1gb of memory for smooth performance, even on high settings
-So when you Crossfire/SLI you won't bottleneck performance (1gb may not bottleneck a $300 card, but it will two $300 cards)
-It sounds better

SLI/Crossfire mirrors the memory between the two cards, so you still have the same amount of memory as using just one.