In my opinion, the only thing the piano and organ have in common are the white and black keys. Everything else makes them very different instruments.
The first rule is that you cannot play the organ like a piano and vice-versa.
And, learn how to pedal before doing anything else. Knowing how to pedal will greatly behoove you.
When I first started playing organ, I had trouble with fast songs as well. To start with fast songs, though, find yourself a good walking bass line. Run your bass line on the lower manual (or upper if you prefer) and play the rhythm chords with your right hand on the other manual. If you're running your bass line well, everything else will fall into place.
With the pedals, I usually tap 1, 4 or 5 or alternate from 1-5 or 5-1 to keep a steady beat. Sometimes, if I'm in the mood, I'll run bass with both my foot and left hand.
As I said earlier, if you know how to pedal, you can completely run your bass line with your foot, leaving your right and left hands to embellish with unlimited possibilities.
The easiest way, though, is to pull up a chair next to an experienced organist (and don't be bashful about doing so). My first day at my church here in Tallahasse, I pulled up folding chair and watched. That's the best way to learn.
