The proper water temperature is 131 degrees faranheit to wash your all your laundry in. Actually, the hotter the better. This will assure that all bacteria and dust mites are killed.
While it's probably a matter of personal preference, it is generally recommended that new sheets be washed to remove the dressing from the fabric. It also makes them a bit more comfortable to sleep...
Definitely yes. There is chemical residue left over from the dyeing and manufacturing process - same with new clothes. Your skin is your largest organ and you don't want to be absorbing those...