Shore power with EPU

The weather is getting hotter and I dont like idling my Lone Star if I can avoid it. It has an EPU and a shore power plug in. I air fry a steak for myself 4-5 times a week and make coffee every day and for that I need to run the truck for up to 20 mins at a time. Inverter says AC bypass 115VAC, 60Hz, 20A.

My plan is to connect a harbor freight predator 3500 generator and use the remote start to fire it up when Im cooking and in the morning.

Will the shore power charge the EPU batteries?
Will the shore power bypass thru the inverter so I can run the air fryer without starting the truck?
What about running the HVAC for extended time without starting the truck?
Will I need to plug the generator in to the plug before use every time or is there a way to connect it more permanently?

Any sources of information from the manufacturer would be great too. I found info that led me to believe shore power was designed to be used with a generator but I cant find that info anymore.

Thanks.

 

This video I guess sheds some light on the topic