1) Yes, the Streams must resume after the network issue has been resolved.
Propagation process tries around 16 times and mark it as not reachable.
So, If the network is down for long time, then it may not restart the streams automatically.
You may have to restart the process in Apply / Capture fashion.
2) Refer to Ans 1)
3) The pending messages will be accumulated in the Capture queue until the destination is available.
Once the target up and reachable the messages will be propagated.