Firstly, welcome.
Secondly, the help links at the foot of most of the pages contain lots of valuable information as do teh HSX Fan Sites (under Community).
Thirdly, to your questions:
1) To my understanding, the Strike Price of the Call and Put options and the Initial Price of the Opening Weekend Warrant is based on the price of the stock around the time they are put on the calendar (rounded to 5 million). The Call and Put cash out is based on the actual weekend box office for the movie, for example if the strike price is 5 and the film makes 8 in its first weekend, the Call will cash out at 3 (8-5) and the put will cash out at 0 (because 8 is more than 5). If it had made 3, the Call would have cashed out at 0 (because 3 is less than 5) and the Put would have cashed out at 2 (5-3)
2) The TAG for a Star at the simplest level is the average Box Office for their last 5 films that reported their takings. It only gets updated once a week and the most recent film only gets included after either its 4th weekend (for wide releases) or its 12th weekend. There are slightly different calculations if the star has less than 5 eligible movies, but you can read about those in the glossary.