Hi flump,
Stats are only recorded to your account when you played ranked games and you must finish out the round in order for the stats/scores to record. If the score is recorded on your history then that means stats have been saved. Practice rounds do not count towards your stats or scoring average. Make sure you are playing ranked stroke play rounds and you will see changes to your stats after each round.
For the long drive to count the ball has to stop in the fairway or on the green. If it goes on the fringe or off into the rough it will not count. Again, if the round is a practice round it will not count at all.
Your scoring average is based upon your best 10 of your last 14 ranked rounds. Based on your most recent scores (41, 38, 41, 46 etc) your average appears to be correct. Your average is an 18-hole figure, so when you complete a 9-hole round your score is doubled and then added to your average. For example, when you shot your most recent 41 it counted as an 82 for your average.