For his fitness- building up muscle and the like, it will simply take riding him EVERY day. My trainer gave me this regiment when I was working to get my horse into shape. There is a TON of trot work. When trotting, make sure he is in as much of a frame as he can hold for an extended period of time. Start by doing 20m trot circles at each end of the arena (A and C) and in the middle, B and E. Do this two-three times in both directions. Then do three trot circles along one long side of the arena. The should be 10-15m. Bigger when you're starting, but work down to smaller sizes once he begins to shape up. Do the the three circles at M, B, and F, and the cross the diagonal and do another set of three circles at H, E, and K. Repeat.
Then do it again, but shoulder-in in-between the circles. Then do it again, but with haunches-in and sit the trot during the circles. Then continue straight and pick up a controlled, medium canter. Do one 20m circle at the top of the arena, either A or C, wherever you end up, and then canter ONE time around the arena. Change reins and do the canter exercise in the opposite direction.
Then do this entire process every time you ride flat. This is especially something you can do on your own. For jumping, I STRONGLY recommend working with your trainer, to bring him along right. But working yourself slowly over poles and just slowly exposing him to more and different types of jumps will help. If he was previously jumping over 1 meter, there is no reason for him to be walking over jumps. He's learned that if he doesn't do it, you'll let him get away with it and take the easy way out and walk over them.
This may have something to do with your position when approaching the jumps, are you leaning forward or resting your weight in your hands on his neck? Are you sitting back the entire time before the jump? Are you squeezing before the jump or just throwing yourself into a two point and hoping he'll jump? You need to ride him right up to the jump, keep your leg on, and in the last three strides, squeeze-tight, tighter, tightest. Unless he is in pain, there is no reason an already proven jumper is not jumping.
Good luck, it will take a lot of work, but if you want to do it, I'm sure you can! :)