Yes it would, because it would become a base 1/1 creature instead of a 0/0 and still have the 2 +1/+1 counters on it. It would then be a 3/3.
Yes, Humility removes the Graft ability that causes the spider to have counters as it enters. This prevents the ability from placing those counters on it as it enters the battlefield. It will enter as a base 1/1 spider mutant with no abilities and no counters.
Yes, if humility left the battlefield, the spider from question 2 would now be a 0/0 creature and die due to having 0 or less toughness. The spider from 1 would be back to being a 2/2 due to the counters.