if you can find it there's a skill video by Fabien Barrel that will help a ton. Seriously one of the best instructional vids ive ever seen and he covers everything from the basics to advanced riding techniques. I think somebody posted it on here awhile back so if you do a search you'll probably find it.

Manuals i cant help you still workin on those myself.

Bunny hopping IMO is directly related to upper body strength and technique. How far you can get the front end of the bike up is going to determine how far the back end will come up. Basically your picking the front end of the bike up at the same time while almost jumping and then throwing it forward to get the rear wheel of the ground. Practice makes perfect. Also try bunny hopping off stuff like speed bumps etc it will help to get the timing down.

For rough downhill sections line choice and stance are key. Once you pick a line stick with it and always be looking ahead. As far as stance goes you wanna be low and off the back seat of the bike heels pointed downwards. Also no deathgrip on the bars. Having a somewhat loose grip will help absorb impacts and keep you more fluid though out the decent.

Pumping the backside of obstacles is just that. Basically just pushing off the obstacle as you roll over it giving you more forward inertia. It does take timing. Again practice makes practice makes perfect. After awhile youll be "pumping" off of everything with out even thinking about it.

Having a full suspension bike helps. Especially in rough terrain. But its not 100% necessary. Though i wouldnt ride my local trials without one i always see people shreddin on hardtails. So i guess that one really depends on the rider.

please keep in mind this is just what i have found to work for me others may have a different answer.