Is there any way to execute 64-bit programs on a 32-bit computer?
If you are talking about a 32-bit processor, then no. But if you are running a 32-bit OS on 64-bit hardware, then you can do it with VMWare. A 64-bit guest can run on a 32-bit host, if the hardware supports it.
Bochs should do the trick, but you'd need another copy of Windows to run in the virtual machine. (Some editions of Windows include additional licenses for virtual machines, so you might be in luck.)
Performance would probably be very poor.
No you cannot do this. The other direction is possible through an emulator, e.g. on Windows it is called WOW64.
It is standard practise on platforms that still have large install base of the 32-bit versions of the OS to ship either just a 32-bit version, or both 32- and 64-bit versions.