I've been doing this for years. I don't have the type you mention - I have a bin with a lid, and 2 side panels that can be raised up so the compost spills out and can be shoveled up into buckets or a wheelbarrow. I have a special tool that is like a spike on a handle, with 2 prongs on the bottom. They fold up when I put the spike down in, then they unfold when I lift it up and twist. That helps bring up the composted items as well as worms, and put them on top of the new material.
I compost food items except for meat and citrus. I'm not sure why you are avoiding food items. I chop up melon rinds and banana peels into squares, I use apple cores and other fruit/vegetable trimmings, stale bread & crackers, coffee grounds, and so on. Egg shells are great - but why are you saying you will used "washed" ones? You're adding it to dirt and leaves. Are you concerned that your eggs are coated with something? Then I wouldn't buy those eggs!
You have to wait a while for leaves to decompose, or you have to chop them up in a lawnmower to get smaller pieces, and you have to turn things more often. The key is not to have a huge layer of any one material (leaves, grass clippings, etc.) but to have a mix. Pine needles and pine cones make the mixture extremely acidic so you need to add lime to neutralize it. Where are you getting seaweed from? Are you buying it, or are you talking about leftover sushi? Don't buy stuff to add - that kind of defeats the purpose!
Definitely put it in some sun - the warmer it is, the faster stuff breaks down. If the mixture is extremely dry (as with leaves), then add water. I put in wet leaves and leftover vegetable gunk, and stick the hose in now and then. If it rains and the driveway is covered with earthworms, I scoop them up and add them in - they do an awesome job!
You don't want to bring the compost in the house to use with houseplants, but you can use it with any outdoor pots, gardens, etc.
If you keep the top layer of added materials from sitting there, you shouldn't have a rodent problem. I just add stuff, and every few days I "turn" it with my compost mixer tool - but in your case, you'll be turning it with a crank. Heat and liquid are the keys. But don't skimp on what you put in there! That's the point!
Let me know if you have any questions!