No, but you can create a second instance of the Shelly adapter which is configured with MQTT (and the other one with CoAP).
No, just configure your shelly devices as documented here and the Shelly adapter will handle everything else.
You can re-configure your instance at any time. You will not loose any objects or states and everything will stay the same. Just the communication method changes changes in the background.
It is not possible to connect the Shelly adapter to an existing MQTT broker in your network. The Shelly adapter starts an own broker which is running on the (non default) port 1882
to avoid conflicts with other MQTT brokers on the same system.
If you use generation 1 devices, you are not able to use MQTT and the Shelly cloud at the same time. You have to use CoAP for integration if you want to keep the cloud connection.
Generation 2 devices are able to connect via MQTT and keep the cloud connection running.