Reddit mentions of Portable Imax B3AC 2S 3S 7.4V 11.1V Lithium LiPo RC Battery Balance Charger

Haha, nice to teach someone ;)

You have it the wrong way around. This is how it's supposed to look. And if you unsolder the wires, you also save some space, which is pretty nice on small builds. And it looks nicer.

The nice plastic wrapping is probably some kind of heatshrink tubing. Want to heatshrink your own stuff? Get this. You just heat it up with a lighter and it shrinks to half the size. There is no problem if you take the plastic off and leave it without it, but it's more likely to short on something, a bit less water resistant (in case a drop of water lands on it), and it doesn't look as professional ;)

If you want to solder the motors directly to the ESCs (which I recommend, as it's lighter and looks neater), you can heatshrink them with this heatshrink afterwards.

The balance charger connects to the balance plug and (usually) the main plug on the battery. There are some cheap, low-power chargers that only use the balance plug. The balance plug has thinner wires, so it can't handle a high current like the main plug (which also uses a connector that handles higher current). On batteries the size of your battery, the wires will be almost the same size, but on bigger batteries the main wires are usually quite a bit thicker. The higher-power chargers use the main plug for charging/discharging (several amps) and the balance plug for balancing (usually under 2A). You should charge your batteries at around 1C, which is 1A in your case, so you don't really need a higher power charger unless you want to be able to charge several batteries at once or plan on getting something that needs bigger batteries in the future. Also, most of the lower-power chargers only have a fixed current and can't discharge the batteries or show other useful information. Most of the higher-end ones can show you the current charging current, voltage, time since starting, mAh recharged etc, and can also discharge your batteries to around 40% which is the level it's best to store batteries at.

The LiPo alarm plugs into the balance port in order to be able to measure every cell individually. This means you can't over-discharge any cell (for example if one of them is faulty and discharges faster than the others). You unplug it when you're done flying, and connect the balance charger to the same connector when you're charging.

When you want to buy a balance charger, you have a lot of different options, depending on whether you want a really cheap charger (something like this), an OK all-around charger (like this one), a charger that can charge 4 different batteries at once (like this one), or a charger that can charge 40 of the batteries you're using in parallel at once (this one). Also note that some of them only have a DC input, so you need an external power supply for them. You can for example make one out of a server power supply, or you can just buy a ready to use one.