Am I able to upgrade to Windows 7?

Yes, you should be able to. Core Duos don't support x64, so you'll need the x86 version, but the specs are fine. I have it running on a C2D 1.6 with 2GB RAM and its flawless. The processor in my machine is a little newer than yours, but the Core Duo will handle it no problem.

You should be able to. I run it on my laptop, which is a 2ghz dual core pentium (based on the core 2 mobile) and it runs well. The MS hardware requirments are here

As many have said - if you can run Vista you can probably run Windows 7. If you'd like something official, try the Microsoft Windows Upgrade Advisor.

http://www.microsoft.com/windows/windows-7/get/upgrade-advisor.aspx

It'll also tell you programs that are known to have issues and suggest possible workarounds, if available. For example, it will tell you to deauthorize your computer in iTunes (if you have iTunes installed).