Question about fuse boxes (updated)

UPDATE:

So the advice to just pull the black box out at the top worked. Entire apartment went dark and I was able to work on some switches and am not dead. I looked closer and that box did in fact say MAIN on it so now I know how to work on the apartment in the future. I did come across a new problem though which I will expand upon below.

So in one of the switch boxes I found something I hadn't come across before. It's a 2 gang box with a switch for a bulb and a vent fan. Coming out of the wall was a black wire, a red wire, and a white wire. I would normally assume this white wire was the neutral wire but it was tied in with the black wire as opposed to just with itself. Can anyone confirm that this is a neutral wire? The layout of the switches and their connections was like this

Red wire wall--> switch
Black wire wall-->switch-->switch-->wall
white wire wall-->tied to black wire but not directly to a switch

If anyone needs a picture I can post it after work.


OP
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So I live in an older apartment in New Orleans and it appears to have a fuse box. It has a set of breakers beneath it but that only seems to affect half of the apartment (which I'm assuming is part of an addition). I'm doing some electrical work on the switches (installing wifi switches) and obviously I'd like to turn the power off so I don't electrocute myself .

I assume the fuses are whats powering the rest of the apartment as when I turn all of the breakers off, a bunch of lights still stay on. I've never worked with a fuse box before so I was wondering what the correct way to disable them would be? There are 4 of them in a square and then a black box above them that has a handle that looks like you can pull it out. I can post pictures later when I'm home but if they're pretty standard maybe I don't need them. I didn't want to just start unscrewing or pulling on things without knowing what will happen or if I need specific tools. I just need to be able to cut the power to work on the switches. I figured this was general enough maintenance to be posted on the OT. Thanks.