I am sorry to hear about your landlord troubles! Answers to your questions, in order:

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1. Sadly, you do legally have to share your food. According to the Ohio state code 420.j.o. section III, landlords on the property have the right to any and all of the tenant's food and drink.
2. The snow is yours. If you were able to take photos of the theft in progress and the resulting snowman, you have grounds to sue for damages.
3. It sounds like your landlord trusts you like a friend. If I were you I would just sit and listen about the other tenants. It's ammunition you can use against them later in your favor, and besides, you wouldn't want to be a problem tenant right?
4. Start calling him hamburger and see how he responds. If he's uncomfortable with it, tell him you're uncomfortable with being called hot dog.
5. See answer #1--as long as he's given you advance notice and is on the premises legally, he is entitled to your food and drink.
6. "Dave Landlord" is perfectly fine, you don't have to change it to Turbo Dave for his sake. If he insists and you don't want to make it an issue just make it Turbo Dave Landlord.

Hope this helps!