1) As for storing your fursuit, it's really up to you on where you want to store it.
However, I do suggest that you store it somewhere away from light; that is, any light.
Sunlight, LED's, your houses' lamps, they can all damage the fur on your fursuit.
Fur tends to 'yellow' when exposed to such things.
I prefer storing all my fursuit parts in storage bins; they actually work wonderfully and I highly suggest it.
I store my heads on a table covered by a cloth to prevent color damage.
All my feetpaws are stored on a shoe rack.
Lastly, all my bodysuits are in fact, hung up. This is probably a horrid way to store them but it's really the only solution that I have.
2) Disinfectant. After every suiting session, flip your bodysuit inside out and spray that stuff allover, especially at areas where you sweat a lot. Same with the head and paws. Don't spray the fur, spray inside the garment. Disinfectant can leave a stain on fabric.
As for washing your suit, I highly suggest that you hand wash it. Seek a liquid detergent that is for delicates and is 'whitening'. They usually get the job done. Avoid powders and powerful detergents at all costs. Test scraps to be safe.
3) I, in fact, don't use any heat shields as they are too pricy for me to afford and I generally cannot be bothered. I just simply only go suiting on colder days. Sorry.
For fans, you usually ask the suit maker to implement them for a price. I don't know if it's possible to install one yourself.
Good luck!