1gb of ram is marginal for running Windows 7. 4 gb installed is about the minimum I would recommend these days. More if you go 64 bit. The rest of your components are a bit weak for gaming, but you'll get the best return on your $ by upping your ram and it should address your scrolling lag.
It's your operating system that determines 32 vs 64 bit. Go to Control Panel/System and Security/System and it'll tell you your system type. If you installed a 32 bit copy of Windows 7, it'll indicate "32 bit Operating System", etc.
You can install 64 bit Windows 7 on an Athlon 64 IF you use a 64 bit Windows 7 install disk.