redistribution is quite a powerful tool and i suggest you pick up a good book like "Routing TCP/IP vol1 by Jeff Doyle" to understand the full capacity of routing protocols and redistribution.
Having said that, let me try to answer all your questions:
Lets say for example you have three routers R1---R2---R3. Also, R1---R2 is a RIP network and R2---R3 is an OSPF network. Please note that R2 is running both RIP and OSPF as the Routing protocols. But without redistribution, RIP routes will not leak into OSPF domian and OSPF routes will not leak into RIP domain, Now to answer your questions:
1) If R1 (which is running only RIP) needs to ping/reach R3 (which is only running OSPF), R1 would not have a route and therefore drop the packet. In order to avoid that, we need R2 to leak OSPF routes into RIP. NoW R1 would have route to R3 and packet would reach R3!
But wait!!! for the return packet, R3 would not know how to send it back to the original source address of R1. So PING would still fail even if packets from R1 can reach R3, R3 should also have a return route back. So R2 would also leak RIP routes to OSPF network and NOW everyone is happy! and PING etc would work from R1 to R3.
2) redistribute connected is useful for leaking connected interfaces in the routing protocol *that are not* a part of that routing protocol. For example, in the above example, if R2 had an additional Ethernet interface that was neither a neither a part of RIP or OSPF then you would need redistribute connected in both "router ospf" and "router rip" to leak this ethernet interface in the whole routing domain.
redistribute static is simply to redistribute static routes in the routing protocol
3) NO! You should try and avoid multiple routing protocols as much as possible in your network. Stick to one routing protocols as far as possible. redistribution can cause a lot of confusion and routing loop if it is not planned properly.
The above was only a brief explanation of the advanced redistribution concept. I would suggest to read up a good book on routing to get a more indepth understanding of the concepts! Hope this helps...
