So basically, I have this card called Metropolis Sprite, and I was wondering, after blockers are declared, right before combat, can I use the ability multiple times to make it say a 3/0 or 4/-1 and have it still do damage, but die after?
You can activate Metropolis Sprite's ability one or more times before combat damage is dealt. However, after each use of the ability resolves (before damage is dealt), state based actions will be checked. When this happens the game will look to see if Metropolis Sprite has more that 0 toughness. If it doesn't, it will be put into the graveyard. Then, combat damage will be dealt. If Metropolis Sprite isn't on the battlefield at this point, it won't deal any damage.
Similarly, if Metropolis Sprite is at 0 toughness (perhaps from a prior use of it's ability), there won't be a moment for you to activate its ability again. (IE, it's impossible to get Metropolis sprite to 4/-1 with just the creature's ability.)
No. From rule 704 on State-Based Actions:
704.3. Whenever a player would get priority (see rule 117, “Timing and Priority”), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event.
After the ability resolves to give Metropolis Sprite 0 toughness, a check is made for state-based effects. Metropolis Sprite dies to having 0 toughness is a state-based action that cannot be responded to (and as such you can't activate the ability again to make it a 4/-1) and the game doesn't continue until after it is dead. Only after the Sprite is dead will it be time to assign combat damage, and it will be unable to do so as it is no longer on the battlefield. If it was declared as a blocker, creatures blocked by it remain blocked and can't assign combat damage to a player unless they have trample or another ability that allows it to do so. But the Sprite will not be able to assign any combat damage.
I just feel I should add my 2 cents just in regards to this statement. Other posters have answered correctly I just want to add a little related rules knowledge.
can I use the ability multiple times to make it say a 3/0 or 4/-1 and have it still do damage, but die after?
Yes, you can activate the ability as many times as you can pay the costs. You can, for instance, activate the ability after each time it resolves. You can also keep priority and activate it as many times as you wish.
You just have to inform your opponent you are keeping priority and then activate away. As other posters have mentioned when the sprites get to 0 toughness it is put into the graveyard as a state-based action and when this happen you cannot activate the ability in response to state-based actions, but that does not mean you cannot activate the ability any amount of times before that happens.