I just found out (after about 7 years) that my PC is actually a x86-64 architecture, instead of a x86 processor (AMD Sempron(tm) Processor LE-1250@2.20GHz, 2GB RAM (1.87GB available)). I currently have Windows 7 Home Premium 32-bit installed. Gotta like windows for hiding it out of view in the prestation index details. (Clearly says that 64-bit windows can be installed) I got the PC with Windows Vista 32-bit with a Windows 7 32-bit upgrade option (which I used).

Should I upgrade to a 64-bit version of windows? Would the PC get faster? (64-bits instead of 32-bits means double the speed when moving data afaik?)

I would leave it as is.

Only consider to upgrade if you have more than 4GB of RAM installed, else no, leave it as it is.

With PAE, you can use even more than 4 on 32 bit system. Consider upgrade if: you have 64bit only application, you need to make programs use more than 3 GB of memory, you have specific application you use often which is optimised for 64 bit. Otherwise do not bother.