Clark, I will try to answer your questions the best way I can.
I learned to turn boxes from Richard Raffan's book on "Turned Boxes" and in it he describes the process and shows the tenon on the body. However there is no rule written in stone that says it has to be there. There are certain boxes I turn, egg shaped boxes for instance, where the tenon is on the lid which for me is the small end of the egg. I happen to like the bottom of the egg, the large end, to overfit the small end therefore the small end will have the tenon.
Some box turners I have talked to always put the tenon on the lid so that when the box is open the bottom continues to have smooth uninterrupted lines. So, Clark, I don't think it matters a whit which end you put the tenon on. The most important thing is the form of the box, the proportions between the lid and the body of the box and how well the lid fits on the box.
The fit of the lid brings me to the answer to your second question. By turning boxes from end grain stock, i.e. the grain is running parallel to the lathe bed in spindle orientation you will minimize the shrinkage and expansion due to seasonal humidity variation. This is true only if you start out with very dry wood, and it is best to use dry wood for boxes, and it is true as long as the diameter of your box does not get too large. The larger the diameter the more apparent seasonal variations will be. If your box walls are too thick they will also be affected by changes in humidity more.
I use Dave Smith's alcohol drying method on lots of pieces of wood that are too green to turn boxes from initially. I will rough hollow the box and soak it in alcohol and let it dry for quite a while usually placing my box blanks in the hot water heater closet to help them dry. After they are good and dry I can rechuck them and finish turning the box.
You can turn boxes from wood turned in the face plate orientation where the grain is perpendicular to the ways of the bed and I do. The only thing you must remember is that the wood will contract and expand across the grain much more when it is oriented in this manner. In a four inch box in certain woods seasonal shrinkage can make your lid go slightly oval enough where it can lock on the box body or you can have a twist fit where in one direction the lid is loose and in the other it is snug or even locked on. I always make boxes turned in the faceplace orientation with a loose lid so they can be opened one handed.
I am reminded of a story where an American woodworker is visiting the home of a master Japanese woodworker. He is admiring a beautifully joined and finished wooden box with a sliding lid that the master uses for storing sweaters. The American comments, "This box must swell shut during the Summer?" To which the Japanese master replies. "Yes, that is true but I don't need my sweaters in the Summer."