Do 32 bit apps run slower (on Windows 7) on the 64 bit version than on the 32 bit version?

It will run slightly slower as it has to be run through WoW64 emulation. The difference is probably not significant enough for you to notice, but it is there.

In fact, some applications may run faster. The system itself will have more efficient drivers. x86-64 requires no emulation of 32bit applications, the processor can run 32bit apps natively. Wikipedia actually has a good technical explanation.