First of all, user permissions have nothing to do with whether your OS is 64-bit or 32-bit.
Secondly, many programs want to modify system-protected folders - i.e. write something in System32, Program Data and so on - when they are installing themselves. While turning off UAC is one way to deal with it, I would not recommend doing so. My advice would be to make sure you trust the program you want to install and then run the installer "as administrator". This will remove most of the problems such as what you describe.
There is of course the compatibility issue. Depending on which programs you want to install, some 32-bit programs are compatible with Windows x64, some run in compatibility mode and some (although this happens rarely as far as I know) don't run at all. This also might be a case. If you have questions regarding particular software, please post back the name of the app that's giving you trouble and we'll try to help you with that.