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I’m attempting to replace some switches and have opened up two of the boxes in my bathroom. I’ve found that for all the switches (5 total switches in 2 different boxes) they only use black wires.

In one of the boxes, there are 4 distinct sheathed groups of wires, which each sheath containing 3 wires: black, white, and copper. All 4 of the white wires are joined into a single wire nut, as are all 4 of the copper wires plus an additional one screwed into the back of the box. The other box is the same (but only has 2 switches and 3 sheathed bundles).

I am super perplexed by this setup. When I test for continuity I get it between some of the black wires in one box and in the other box, as well as between some combos of wires within a single box. One of my switches even has a wire jumping between it and another switch (see photos).

If necessary I can try to draw a continuity diagram. Part of the reason I started working on this was because I had one switch that needed to be jiggled to work, but if jiggled the right way, it would turn OFF a light that is controlled by a switch in the other box.

So here are my questions:

1. Is this correct/safe
2. How is this even working when it seems like it’s only using hot wires making one big circuit. Why aren’t any white/neutral wires used?
3. Should I use the ground wires for new switches that have ground connections, and if so, do they need to be matched with the sheathed bundle that has each switch’s black wire, or are they all going to the same place.
4. How can I add a timer switch that has red, green, black, and white connections (load, ground, hot, neutral). (See photos)