0. x86_64 can be 25-85% faster on true 64bit hardware depending on the architecture, the software and compiler optimizations.
This is certainly true on AMD 64bit hardware which is definitely 25-85% faster running most 64bit apps versus the same 32bit apps due to the wider 64bit registers and the fact there are more of them as well as the new instructions added to the architecture.
In x86_64 AMD doubled the number of general purpose from 8 to 16.
The number of XMM/SSE registers was also doubled from 8 to 16.
5. Absolutely right, Linux supported x86_64 immediately after x86_64bit CPUS became available. I've been running it practically since day one. Linux was many years ahead of windows in x86_64 support and arguably still is.