Hi Aqamah
Here are some answers / suggestions to your questions:
1. Certainly GemFire can play a role here. I would suggest that you take a look at some of the Spring Data modules (if you haven't already) which allow for exposing GemFIre with REST services and persisting data to GemFire via JPA, amongst others.
Spring Data GemFire | SpringSource.org
Spring Data - REST | SpringSource.org
2. Yes. You mentioned that you had worked through the quickstart examples which should also have included an example using Function execution. Perhaps if you have a more concrete example, we could give you more specific help.
3 / 4. Not directly - see #1
5. Also, please take a look at the current documentation: vFabric GemFire 7.0 Documentation
--Jens