Isaac, there is some variability, but most seats will stay in place if you push hard then pound with your fist (or a hammer). Once in, I leave mine in place permanently, using the bungees to simply fold it forward for transport. That way, it';s faster to launch and harder to forget. Haven't lost one yet! (btw, the old seats were riveted in permanently).
For the seatback bungee, I clip it to the cargo bungee. As baysailor says, it just keeps the seatback from flopping forward. If you cut off that annoying little lock clip, the hook is real fast and easy to use.
You shouldn't store your boat on the cart -- it will dent the hull. Although it should pop out, I don't recommend it. Store your boat as recommenced by Hobie, but not on its bottom!
Everyone develops their best way to insert and remove the cart, but with loose gear, I find it easiest to wheel the boat right into the water and reach underneath to remove the cart. Or lift the stern and let it fall away. To insert, just reach under the boat and pop it in. With a little practice, it's pretty easy. The cart holes (scuppers) are fairly thin -- make sure you insert the cart in all the way before towing.