1. GPU = Graphic Processing Unit.
2. Yes, you can change that, if you are comfortable with opening your iMac and work inside. There are several Youtube videos giving instruction on how to do. Ifixit also have a full article with photos on this.
3. "How much does it cost" is depend on the seller and the time. Check the link below for one I found at this moment on ebay.
Find many great new & used options and get the best deals for AMD Radeon HD 6770M 512MB GPU from 2011 iMac at the best online prices at eBay! Free shipping for many products!
www.ebay.com
4. Similar to yours, it will definitely fail again very soon.