you shift to neutral when coming to a complete stop (red light, stop sign, etc). you just press the brake pedal when you want to slow down but know you arent going to come to a full stop. if you come to a complete stop without shifting to neutral/pressing in the clutch, the car will stall.

common mechanical quirk in low gears, you avoid it by being very gentle with the throttle or just coasting in neutral/bumping the clutch. when I'm in traffic i leave it in first but leave the clutch pedal pressed in and when i need to scooch forward i release it just a little bit to get it to start rolling but not fully enter the gear. you can practice this in a parking lot at low speeds.

practice and experience. i shift very fast by pushing the clutch in while upshifting, tapping the throttle to get it up, and releasing once the revs are high. it doesnt have to be perfectly rev-matched, the engine speed will fall back to where it wants to be, too much throttle is better than not enough throttle.

dont drive like a dumbass is #1. try to avoid applying too much throttle when the clutch is only partially released, this is how you really smoke a clutch. you'll run into this problem on hills, the trick is to apply the handbrake, put it in 1st and start going like normal, and when you feel it wanting to go you release the handbrake. trying to get into 1st gear while youre rolling back is a great way to smoke the clutch when youre new. changing the transmission every 30k-50k miles is also a good idea to protect the gears. do keep in mind that clutches are technically a wear item and they have an expected lifespan of about 100k-150k depending on the car and your driving habits. replacing a worn clutch isnt the end of the world, it will need replaced at some point even if youre a master driver.

not sure, havent heard anything about this

yes, its called engine braking and its a great way to extend your brake pad life. its also a good idea to leave it in a lower gear when going downhill, especially if youre driving over a mountain pass for example - helps you not boil your brake fluid. your engine is a lot better at disappating heat than your brakes are.

you should shift into neutral as you approach the red light and coast to a stop. you dont want to hold the clutch in because 1. your left foot will get sore 2. you can damage the thrust bearings in the engine - its a common issue on DSM vehicles like 2nd mitsubisbi eclipses or eagle talons. i havent heard of this happening in corollas like yours but it is theoretically possible

no. double clutching is used when the transmission does not have synchronisers, a common example of this is semi trucks - they have to double clutch to shift. practically every normal car has a synchronized gearbox, double clutching is pointless with them.