Answers for your questions...
1. It always synchronizes with preferred server only, if it fails only another routers(peers) will be considered.
2. The PREFERRED peer always get selected over the best stratum server.
3. If the Router (NTP client) is polling a server of stratum N, the client will be stratum N+1 when it synched up. Otherwise, it will stay at stratum 16.
4. For final answer, I believe the answer is YES.