I purchased this mower last year, changed oil, and basically kept in good condition. I want to know what kind of maintence do I need to do for the grass cutting blade and the belt. This summer I bought the twin bagger and whenever I cut slightly damp grass, it always get stuck in the chute and eventually stuck in the mower area. This caused the belt to sound rough whenever I switch over to cutting mode.

1. What do I do to change the belt?
2. How do I know when I need to change this?
3. Is it possible to jack up the mower, or what do I need to do to get underneath the mower (crawling underneath a mower staring at blades sounds scary).
4. What else should I do to prolong the life of my mower

One more thing, when I get off the seat (engine on) the engine cuts off due to the battery connections under the seat, while the engine shuts off, I sit back on and the engine backfires, how much damage is this to the engine?

When you get off the seat, it pops a seat switch... basically safety in case you flip it, etc...
It won't damage the engine, but its not something I'd keep doing to cut it off, etc...

For getting under it, car ramps would be best... or remove the deck (few pins, etc.)... as long as its off, brake on and its in gear... you should have no worries.. do not jack the mower up and get under it... very dangerous.. having 500 pounds or more fall on you doesn't sound good does it?

The belts should last a few years.. kind of sounds like your cutting too high of grass maybe? Or wet/damp? This will make it clog... cooking spray is good as a lube to help keep it from sticking.

Other things to help it last longer... well change the oil regularly... every 25 hours is good, change the air filter every year.. if this engine has a oil filter, every 25-50 hours is OK...

Never use hd-30 below 40 degrees f.
I never use it below 50-55 degrees...
Use either a multi weight conventional below 40, or use a multi weight synthetic all year round.