1) The source IP address is unchanged unless you specifically configure an SNAT or NAT
2) There is no setting, reverse or forward is just terminology to describe usages, the F5 will proxy in either direction by default based on it's general configuration
3) It can do both. Half is faster (or at least less CPU intensive) and operates at L4, full operates at L7. This is decided by the Virtual Server type you choose, a standard VS is L7.
4) As I said, forward or reverse, it doesn't matter, proxying either way provides many benefits. For more information, browse through the F5.com site, there's plenty there.