I think that these should be open to suscribers only, though only the Rookie one could realistically be one by a non-suscriber. Another benefit to subscribing.
I really like the Rookie one. You have to have gained your non-provisional rating during the month, and the rating at the end of the month is the criteria.
Highest Rating, no. This doesn't change enough.
Instead of most active tournament and clan player, how about best tournament/clan player. This would be based on record and require a minimum of 5 completed games. Low rated players could win by participating, and doing well in, the banded tournaments.
As for most improved. I don't think measuring a one-month difference is the way to go. I think that should be measured over 6 months. Using trend-line analysis over the last 6 months would show who had improved the most. To cheat here, you would have to force-feed yourself failure for quite some time and then improve.
Have a rule that you can only win each rating-judged category once evey 3 months.
I really like the most-valuable clan player. Give a tool to each clan leader to manage that.