Jeri, you have asked a lot of interesting questions and I hope I can remember them all to give you my opinion on them.
1. If you have a choice, I would have the tile installed first. Until you actually have the tile installed, you will not know exactly how high it will be. If you have a deeply textured tile or stone installed, this could vary quite a bit.
2. You will be running a wood molding/capstrip along the top of the wainscotting. Why not just turn the molding down so it covers the exposed edge?
3. I think it will look a lot better if you put some kind of base molding on. It will look a lot more finished and leave a strong demarkation line between the wall and the floor.
4.I really have a problem here. Your hallway is probably pretty narrow already and the dark green will just make it smaller. It you are really sold on the green, then paint is the only way to go. But, if I were you, I would look at a lighter color choice. Minwax makes a line of colored stains in many pastel colors that might give you a place to start. I have been having a "Mission Crisis" for the last several years and think everything should be Golden Oak, but the kind of wood you choose for your wainscotting will determine or limit your choices of stains. In any case, you should put 2 coats of a matte finish on it and water based polyurethane would be a good choice for this.
Good luck and have fun deciding and doing it. :o) Henry