Office 2007 works fine on Windows 7 - FWIW I have Word 2003, 2007 and 2010 installed here.
It is imposible to guess what you did that screwed up Office 2007 on your old PC, but it sounds deeper rooted than simply the Office 2007 installation.
Office Starter is installed on a virtual disc - a Q drive - and so should not interfere with the Office 2007 installation which will install on your C drive. Personally I would uninstall Starter, but be aware that if you do that it is unlikely that you will
be able to restore it without returning your PC to its as supplied condition i.e. without your software and data.
If you retain Starter there will certainly be some conflicts over shared resources. It seems likely that they will share the same normal template (which is not a good thing), but if you rename the normal template and don't use Starter at all, it should be OK.
You will almost certainly have a Office 2010 trial on the PC, either installed, or ready to be installed. That must be removed or you will not be able to activate Office 2007. You can always get a new trial later if you wish to update.
Fonts are stored in the C:\Windows\Fonts folder. Simply copy the relevant files from that folder on your old PC to the same folder on the new one.
I think all your other questions have been covered.