1. Yes
2. Depends on what method you use to spawn the reverse shell, you have many options. You may use a simply netcat listener, a meterpreter payload handler, PowerShell empire payload handler, etc.
3. In the post-exploitation phase you could upload mimikatz, or, if you are using something like Powershell Empire to spawn the reverse shell then that functionality is built right in, and can be loaded right into memory without ever touching the disk (AV bypass).