1. I assume it depends on the nature of failure and how far it progressed. It is possible that during power-up the chip goes through various quick test to verify it's fully functional. If even one of them fails, it will lock up and refuse to continue. However, during normal operation, some of these paths (which may be faulty) may not be used, except in very specific scenarios. This would explain why, if pressure tricked the device to pass the power-on tests, the laptop can function normally for a long time.
2. Some do, some don't. The ATI 7500 boards do not, presumably because the chip is considered less power-hungry / hot. The ATI 9600 / FireGL boards use the long heatsink which covers the GPU. AFAIK, it is possible to mount the long heatsink on the 7500 board, as an aftermarket solution, which may (although not consistently) improve the longevity of the chip.
3. It is not required, per se, not with desktops, nor with laptops. With that said, not all thermal compounds are created equal. Some, even after years, do not dry up and continue performing just as well. Others do dry up and become less effective. AFAIK, the stock white compound used by default on genuine Thinkpad heatsinks, unfortunately, happens to be of the latter, poorer quality. "Refreshing" aside, many forum members will tell you that better cooling performance can be achieved by replacing it with better paste (Shin-Etsu, Arctic Silver, or a few others).
3a. With that said, I have not witnessed overheating CPU being a common issue with T4x Thinkpads. But, in any case, you can (and probably should) install TPFanControl to monitor your temperatures, and if you wish, modify fan behavior.
Current: X220 4291-4BG, T410 2537-R46, T60 1952-F76, T60 2007-QPG, T42 2373-F7G
Collectibles: T430s (IPS FHD + Classic Keyboard), X32 (IPS Screen)
Retired: X61 7673-V2V, A31p w/ Ultrabay Numpad
Past: Z61t 9440-A23, T60 2623-D3U, X32 2884-M5U