ZvZ, 9 pool vs X mentality

There are two different scenarios that can occur here. Your opponent could go for speed first or lair first.

A. Speed first (opponent)

Since both players are playing identical, you can approach this in different ways depending on how confident you are in your micro and multitasking skills. If you are self-assured, you can be really aggressive and try to gain advantages this way.

Another way is to, once you establish both of you opened with 9 pool speed, try to make extra drones with the eventual goal of a second hatchery in your main base. The advantage of having extra larva can not be understated.

B. Lair first (opponent)

Since your opponent forgoes speed, he will lose map control and it will be very dangerous for him to move out. Most likely your opponent will therefor be defensive and block his ramp with lings. By doing this he can try to gain an advantage in drones. This goes hand in hand with skipping speed all together. In my opinion it makes more sense to ignore researching speed if you're going to be defensive and try to squeeze in more drones.

What to do in this situation? I think it is very critical to constantly observe what he's making. Is he making drones or lings? If he's getting really greedy busting his ramp with lings can work. However if he's being safe and adding lings, it will be very difficult to break the ramp and it can backfire very easily if he did decide to research speed anyway.

And what to do about the impending mutalisks? I'm not sure whether you are in trouble or not. I think the difference in spire timing is about 30 seconds which could mean that mutalisks are already in your base when yours spawn.

THUS: What should you do in this situation? Block his ramp while you try to squeeze in drones? Take a risk and make only zerglings with the intent of busting his ramp? What about the incoming mutalisks?

There are again 2 scenarios:

A. Speed first

You are behind since your opponent has one more drone, which really adds up. He can decide to keep it on gas (less likely) or utilize the extra mineral advantage to afford a second hatchery earlier.

What to do in this situation? First of all, it is quite difficult to tell whether your opponent is overpooling vs 9pooling since the only telltale sign is the amount of drones that he has vs the amount of lings that he has. It is possible to conjecture his opening on the timing of his lings, but it's possible for him to hold position with his lings in his main to deceive you.

In my opinion, your best option is to play defensive, block your own ramp and try to make drones (1-2, more if he's droning as well) as soon as possible. Making purely lings is a risk where you're hoping to get a get a favorable fight, which might not happen.

B. Lair first

This situation is very much equal to the situation of 9 pooling into lair first. The only difference is that he'll have a slightly better economy but his mutalisks will be noticeably later.

I think that in this case there shouldn't be an issue of mutalisks being in your base already when yours are about to spawn.

In my opinion you have one big opportunity as a 9 pool player vs 12 pool (much better on maps with lots of open space around the natural). The moment you have speed, your lings can win a straight up fight, which also happens to be an opportune moment as his larva advantage hasn't kicked in yet.

The other way to approach this is to play more defensive after threatening with speed (you want him to make lings and not drones), using ramps to your advantage. A 12 pool player only has a one drone advantage (10 vs 9) so you by making a few drones and getting a second hatchery as soon as possible in your main, you should be able to level the playing field. Then it will be a matter of being as aggressive as possible to prevent him from utilizing his second gas.

As a 9 pooling player you are at big advantage depending on map distances. I believe destination is just large enough to allow your opponent to get a sunken up in his main with minimal losses. He will be forced to cancel his natural hatch. The result for him will be no speed, delayed tech and only one hatchery. He will be able to put up his second hatchery in his main relatively soon though.

I believe the best course of action is to after your initial aggression make a few drones and get a second hatchery in your main. I have in various situations tried getting hatcheries at my natural but they're often an unnecessary risk. They can be canceled relatively easy which is deadly (same when playing 9 pool vs 12 pool)! You need those extra larva or you will fall behind. Now you can use your earlier mutalisks to try to do damage or outright kill him, or secure your natural.

I have no experience yet with overgas, I don't know the timings or even the correct build order.

Opening with 9 hatch gives your opponent 8 zerglings before your 6 zerglings arrive at his natural. You can not stop it. This opening typically aims to all-in with zerglings by building up an unexpected number of zerglings. As a 9 pool player you have map control for a short period of time. At the moment you are also at a drone advantage (9 versus 7). It is however very important to check what he's building with his larva. He has 2 hatcheries so can pump out a lot of drones relatively fast. However, since his tech is so delayed he will be forced to get spore colonies.

If he's building nothing but lings, you can make 2 or even 3 sunkens and continue building lings. You just need to hold his all-in. Your mutas should be able to end the game.