Validate off-grid power solution for a food truck

Please review the attached project brief and let me know if this falls within your area of expertise.

Off-grid power solution for non-stationary food truck

To recharge the battery:
we will plug into the grid power during operation, whenever possible;
we will use the generator, whenever the truck is in a non-grid location or on the move
lateron we may add solar power on the rooftop

In either case, the inverter should stop charging when the batteries are fully charged and allow batteries to drop to 50% level before charging again

At all times, the food cart appliances are drawing power from the battery pack

The combined running power required for the operation of the appliances is around 4500 watts

What I need:

Validate the proposed diagram above for a 5000 watts requirement
Calculate the load flow
Calculate the generator power required to operate the system 8 hrs per day
Recommend type of battery pack, specifications and capacity requirement
Draw a connection diagram including necessary switches
Make additional recommendations