Welcome to fish forums!
1. if everything is working fine, then i would keep it, no need to spend more money on something that works perfectly fine
you can also use a toothbrush to clean off the mineral deposits.
2. we get that crusty stuff too, i usually just wet a towel, scrub it off, and then i be sure to dry it off, without throwing it in the tub.
3. if you decide to keep the filters gravel, and other decor/acessories, you should have enough bacteria to skip the cycle as shev said. but i would be cautious of a mini cycle. just to be safe.
4.hm if it wont fit in your car, i would get towels and wrap them around the tank. maybe bubble wrap too. (and i would be paranoid haha)
good luck!