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I made a post here about how to use RuneLite with the Jagex Launcher. Tutorial - Jagex Launcher Fix!
Send your purchase IDs to @Arbiter in PM and he'll review when he gets a chance.
If you make changes to any code related to the other two bots, they'll be re-evaluated by the bot pusher.
The client itself isn't updated automatically on game updates because there's nothing to update, but the bit that actually speaks to the game...
Payments within the last calendar month stack - so indeed, if you paid $3 10 days ago, and another $2 today, your "effective" payment would be $5...