1. I would think 3' or better where you are would be more than sufficient. I would do gravel under mine as someone above said.
2. I like to concrete mine in dry, you will get answers all over the map on this one, personally, I am not sure there is a "right" way. I am assuming you already have the posts, but if not, try and find .6 Pressure treated (lots of nasty chemicals in them) Posts. .4 is what you will find at Lowes etc. I believe that will make more of a difference in the life of the post in the ground over if it is in concrete or not.
3. You need to set up batter boards and string lines. From your questions, I am guessing you are going, what the heck are batter boards (If I am wrong, my apologies) If I am right, google about a bit, or look for a house they are pouring a foundation, footing on. Look about 3 to 4 feet outside the edges and you will see about 4 ea 2x4's pounded in the ground vertically and two 2X4's nailed to them horizontally (and hopefully level) Then on the top of the horizontal will usually be some double headed nails. Your string line goes on those nails, and represents where your building edges go (or post edges, or whatever you are trying to line up.) Anyway, once your batter boards are correctly set, you use them to set your various posts, and honestly, it does not matter in what order you set the posts once those lines are established.
Hope that made sense, and sorry if you knew it already, I may have just misread.
Good luck, it is always rewarding to do something your self.