If a indestructible creature is a 3/3 and I block that creature with a 2/2 then I give the indestructible creature a -1/-1 will the indestructible creature die?
Don't confuse reduced toughness with damage. Damage gets marked on a creature, but it doesn't reduce its toughness.
The 3/3 takes two damage, remaining a 3/3. then you reduce it's power and toughness with the -1/-1. It is now a 2/2 with two damage marked on it. However it is indestructible so this is not sufficient to kill it. You would have to give it -3/-3 for example (reduce its toughness by 3)
702.12a. Indestructible is a static ability. 702.12b. A permanent with indestructible can't be destroyed. Such permanents aren't destroyed by lethal damage, and they ignore the state-based action that checks for lethal damage. 702.12c. Multiple instances of indestructible on the same permanent are redundant.
No. Once damage has been dealt, the indestructable creature is a 2/2 with 2 damage on it. That means it has lethal damage, but that doesn't mean anything for an indestructable creature:
702.12b A permanent with indestructible can’t be destroyed. Such permanents aren’t destroyed by lethal damage, and they ignore the state-based action that checks for lethal damage (see rule 704.5g).
So you need to either lower the toughness of the creature further (to 0 or lower) or remove the indestructable ability from the creature. Damage isn't helping here at all.