1. What do “reward system” and “statistical system” mean, and why is Puzzle Ratings a reward system?

A rewarding rating system mostly rewards participants who participates in the most number of events. This doesn’t mean that the people who participates the most will have the highest rankings, but it does mean that participants rarely loose points after an event. For example; tennis ratings.
A statistical system always adjusts participant’s points after every event. Either rewards or punishes. For example; chess ratings.
Puzzle Ratings is a reward system just to attract more people into puzzling and into participating in puzzle events. More the participants, more the enjoyment. This system is also punishing very low scores, and it also has a statistical behaviour by giving Bonus/Penalty points.
Also note that this system may be changed to a statistical one a few years later.

2. What are those approximate rating points in the “calendar” links on the left, and why are they different even for the same competition?

Each competition has a constant number as presented on the “competitions” links on the left. This constant number is added to another number, based on the difficulty of the individual competition (e.g. PQRST 12), totalling up to the value of the competition. In some cases the rating total of a puzzler may be over 100 when he/she gets bonus points. Therefore these numbers can change even if the difficulty stays the same.
Also note that given numbers are only predictions, just to give you an idea.