For a player that is in the gold league, your initial build orders seems very solid, at least a lot better than other gold zergs that I have met before.
One fundamental rule that you have to remember about ZvZ is this: Anything can happen at any point of the game. ZvZ is the most volatile matchup out of any other possible ones largely because of Zerg's capability of producing a massive amount of units quickly. For other matchups, given enough training, you are able to narrow down or at least get an intuitive feel on when your opponent may attack you. In other words, there are a definitive set of "timings" for the attacks you can expect but this simply isn't the case for ZvZ.
Consider this: For ZvT, even if you didn't know 100% of what your opponent is doing, you have the option to be a little bit greedy and pump out drones as long as you don't over do it, because it actually takes a while for the terran army to march all the way down to your base (This is why creep spread is crucial in ZvT). For ZvP, there are only a limited set of potential timing attacks that is employable by the Protoss, such as 6 gate, blink stalkers or the dreaded parting style all in. For ZvZ, none of the above I talked about applies, because it takes seconds for the Zergling army to arrive to your doorstep and they are very easy to produce.
Now I will apply the above principle to the replays you have uploaded and talk about the specifics:
Here's a replay where a bunch of zerglings stream into my base at the
5:40 mark. My overlord sees this coming, so I try to squeeze out a
spine, block my ramp with my queen, and take an extra gas so I can
support more banelings. I start morphing some banelings as soon as my
baneling nest is done, but there are just so many zerglings that I
can't hold off his reinforcements.
The opener you scouted your opponent is the infamous aggressive 14/14 and happens to be my staple build order. Since you opened with a pool first then hatch, there should've been only one thing that crossed your mind: He will attack me in the vicinity.
And your response? You kept droning... and you waited until the last moment to start producing Zerglings and a spine crawler.
And this is basically what ended up happening:
You might be thinking, "But hey, what if he didn't attack me and instead decided to heavily drone?". Well, there is an important lesson to be learned here. You need to consider both of the worst case scenarios that could happen if your opponent had put the aggression on you vs if he didn't decide to be aggressive and start droning himself.
- Opponent Attacks: You lose the game (At the minimum, you lose drones and/or queen, putting you behind).
- Opponent Starts Droning: Both of you are at an equal worker count.
Really, it comes down to a simple logic like that. Now tell me, being a pragmatic and a logical player, which one of those cases sound better to you? In fact, it is more likely that you would be slightly ahead in drone count even if your opponent had started to drone because you had your hatchery done first.
But what if you screwed up somehow and overcommitted with the zerglings? No problem, put some pressure on your opponent, prevent him from droning and in the process, start making drones for yourself. This process goes back and forth in this volatile matchup.
Other problems I wanted to address are your mechanics and map awareness. You state that you blocked the ramp with the queens. In fact, you didn't properly block the ramp because you sent your queen from the main down to the ramp way too late.
You built a baneling nest, which is a good response but during the aggression, you didn't realize the building was completed and didn't accordingly start to produce banelings.
In fact, because your opponent carried out the attack somewhat badly, you could've easily defended that attack at the moment the enemy lings left his base and be substantially ahead in the game.
Since I happened to have some Korean DNA embedded in my body, which means I get a racial passive bonus in ability to play Starcraft well, I am luckily able to demonstrate this point. Blizzard recently implemented a very nice replay feature which lets other players take over in any desired point of the game. I've asked my brother, who is a top master player to take over as your friend.
Now that I've extensively covered one replay, it gets easier to answer the remainder ones:
In this game I attempt to go spire. This game, I made as many
preemptive banelings as I could afford. I figured he would be low on
the tech tree, so mutalisks would be able to deal with his tier one
aggression. But he was droning behind it, and eventually overran me
This one is easy. You were so severely behind when you cancelled your first hatchery that it is safe to say you practically lost the game at the moment the hatch was cancelled. The thing is, that hatchery did not need to be cancelled at all. You could've let your hatchery tank a bit and buy more than enough time to produce 2-3 sets of lings to defend that light aggression (more like scouting in my eyes).
Here's a replay where I make it to lair. He floods my natural with
lings at 8:00 but I manage to hold onto my main. However, he was
droning behind it, with roaches on the way. His two bases vs my one
base was a situation I couldn't recover from. I was floating a lot of
minerals and idle larvae in this game though. Maybe that was my
Recall the most important fundamental rule I have reiterated over and over: Anything can happen in ZvZ at any given point of time. Ever wonder why professional players would make few banelings and a spine crawler at his natural when both players are in fact, droning? It's because of this very possibility from being overrun by the zerglings and losing the game.
The banelings play a critical part to buy you enough time to produce more lings and spines to defend yourself. And there's no reason that you couldn't because as you said, you were floating on a lot of minerals which is another sign that you need to improve your mechanics.
I also have a fourth one. Same deal. He floods my base with lings, I
lose. I saw he had no expansion by the time I had mine up, so I
prepared some defensive lings. However, when I saw him expand later,
and my overlords saw nothing suspicious, I thought he had made a
hidden expansion somewhere on the map. I still made as many banelings
as I could afford right when my baneling nest completed, but his
stream of units still destroyed me.
Same issue as #1. You were droning hard when you should've been making zerglings and banelings.
Regarding your thought of a hidden expansion, you should've completely ruled this possibility out when you scouted his 14/14 build. It is illogical to build a proxy expo in the early game where each other can be scouted very easily. Unless if the sun rises from the rest and the moon turns red.
Your general understanding of the game seems to surpass that of a typical gold league. If you consistently practice your mechanics and try to logically deduce why your opponent might do A or B, then you should be able to hit platinum or diamond league asap.
Additionally, please read this matchup guide posted from Teamliquid. It should give you an insight of how ZvZ works generally.