Electrical – this black cylinder on the side of the electrical junction box

That looks like a doorbell transformer. Those smaller wires should lead to your doorbell chime unit (assuming you have a doorbell). The junction box is there simply to provide power to the doorbell transformer.

From the picture it looks like you have 12/3 and 14/2 in that box, but it is difficult to tell. How confident are you the larger wires are larger than #12?

Figure out what breaker is supplying power to that circuit. As long as it is sized appropriately for the smallest conductors on the circuit, it will be fine. For example, if that is indeed a mix of #12 and #10 copper, your breaker must be 20A or smaller.

Also as a side note, NM cables entering that metal junction box need to be secured with a cable clamp. Any unused knockout holes need to be plugged. It looks like you've got a couple of code violations there at the top of your picture.

You are almost right

The solo black wire is indeed the switched hot for this circuit and the junction of all white wires is indeed your neutral. However, you shouldn't tap ground at the box screw, but in the wirenut with the bare wires in it (in the back of the box) -- the box ground screw isn't intended for two wires at once.

P.S. the other junction (one white and rest black) is where the always-hot is -- the white wire in it carries the always-hot to the switch in an old-style switch loop configuration.