Taking your questions one at a time.
Don`t keep paint or cans of spray in it.
It depends on what you want to grow whether you heat it in winter
To keep unwanted pests out, tell the wife to stay in her kitchen,........ no seriously, you could hang a fine net over the door and louvres and roof vent. If you intend to grow tomatoes and cucumbers in it, you should keep them apart by making a separate compartment somehow as they like different conditions.
I`m sure you will get much more advice from others,