Do you need a latch if it's inside a secure run, no in fact a lot of people don't even use doors when the coop is secured in a run, but beware raccoons are clever, and resourceful, multiple lines of defense increase your odds the chickens will be safe...
It could be as simple as a metal rod with a small hoop at the end, attached to the door and when closed, the hoop aligns with an eyelet in the side of the coop that allows you slap a lock trough both hoops and secure the door shut...
Don't bother or waste time sealing the cracks, the wood will twist, expand and contract and new ones will just appear... Also if you insist on sealing I would advise against silicone, polyurethane caulk is better suited for this purpose and you can easily paint it...
You can put the food...