Points can be allocated as part of a prize or through a number of other means, such as for buying-in, for rebuying, for busting other players out, etc. So, points listed on the Players tab are points that a player has earned in the tournament. Points listed on the Prizes tab are points specifically awarded as part of a prize.
As for Stats, if you see NO players listed on the Stats tab:
- Make sure you've refreshed the tournaments (Refresh Tourneys button)
- Make sure the players you expect to see are in your player database (only database players show up)
- Make sure the tournaments you expect to get stats from are done (the tournament has ended)
Press the Info button to see what tournaments are being loaded and which ones are not, and which of the tournaments that are loaded are passing the filter and which aren't. Loosen up the filter if necessary by changing the various filter attributes to "<any>" and leaving the Date fields empty. This should catch all of the tournaments.