Have a computer running windows 7.  I saw that the operating system requirments is windows 8.1. Will using windows 7 cause any issues with easy worship?

Also wondering if GeForce 8800 GTS is compatible with Easy worship 7.

The latest releases of EW7 will not run on Windows 7. You will be limited to release 7.1.4.2 and previous, with 7.1.4.2 highly recommended. You can download that from the regular EW7 download page. The link is at the bottom of that page. 

At best you might be able to run a minimal instance of EW7. That means only a FOH display and the main control display. NO Foldback. Text and static images only. No motion backgrounds. And limited to 720p resolution. Definitely not an optimal situation, but you might be able to squeak by while saving up for a better Graphcs Card. 

And it would depend on the rest of the hardware in the computer as to how well it would work. If the CPU is at least a 2nd gen Core i series Intel i5 or i7 processor and at least 8 gigs of ram you would have a better chance. If it's an old Core2Duo or Quad from the same era as the 8800GTS and 4 gigs of ram or less the chances are rather slim even a minimal instance outlined above would work out well enough to be viable.