You can add a second transfer switch or plug your cord in direct.
Do not just tap into the existing switch.
Your entire panel will be powered so you will need to turn some items off such as converter, fridge, electric water heat and microwave. Worst case you will run the battery dead quickly or overload the inverter.
If you want to power a single branch circuit you can use a small 15a transfer switch after the branch breaker. Then you end up pulling 120v wire to the panel. Or you can move the inverter to behind the breaker panel and just use the main 12v battery feed and connect to the branch without pulling wire.
Yes you need to use the chassis ground. Connect direct to the frame independent of other connections.
Nice inverter BTW :B