If you Stop replication - this effectively means that the destination files will be removed. So you don't want to do that 
Pausing replication means that no changes are send to the target location.
Actually you can recover the VM w/o powering it off by choose the setting in the recovery wizard for not doing sync
Once the VM is recovered and added in the VC inventory it is a normal VM and you can connect it to what ever network you want. The network configuration is not part of the vSphere Replication product at all so you need to search for another mechanisms - manually through the UI or using PowerCLI or vCO
Hope this helps