My inverter has a chassis ground stud in addition to the normal battery + & - connections. Should i run this ground to the engine block, or can i just run it to the battery too? When i was doing my wire testing, it was working fine w/out it, but i figured i better connect it to be on the safe side.

It should be connected to the chassis ground on the shore power panel.

My panel is grounded to a main bus bar that other things are connected to. This i am sure goes back to a block. so i will just run it directly to the engine.