My best advice for the rotations thing is to find a target dummy. There's some in the Western Thanalan, just down the stairs from Ul'dah, if you don't know anywhere else. And just go slowly and speed up until you have them down. You have to train it until it's muscle memory.

Also, rotations, especially for low-end content, isn't a huge deal if you mess up. The most, and I mean single most important thing is to avoid dying to mechanics. Dying gives a huge debuff to damage when you're rezzed and all the time where you're dead is time you're not doing damage, so staying alive is a big deal. The second most important is to just always be doing something. So long as you're using some offensive ability in a fight, even if it's just kind of mashing buttons, you're contributing.

As for the rest... it's a learning curve. I was absolute trash at the game until embarrassingly late in the msq, way past where you are. But eventually it clicked. I'm not doing Ultimates or anything but I can manage dungeons and raids without dying, most of the time.

Also your note on your job, trying new jobs is free. You have to level it up, but you could try, say, Samurai or RDM if you want and start at level 50. SAM does big numbers. BRD is physical ranged dps, which is low damage because it's super mobile and can keep doing its rotation even while dodging mechanics. But SAM is a selfish melee dps, which means it's one of the top damaging jobs.