Are the breakers adjacent? If so, you're probably looking at a multi-wire branch circuit which should--but doesn't--have an approved tie-bar device between the two breakers, and which would use one neutral for both sides of the circuit.
Multi-wire branch circuits are safe when both branches are powered and when both branches are off. They can in some cases be dangerous if one side is powered and the other isn't.
If this isn't multi-wire branch circuit wiring, I doubt that it's safe at all. It appears that black and blue are two hot wires entering from #5, which has one neutral return. If black and blue are anti-phase, as in a multi-wire branch circuit, the maximum current on the neutral will be the difference between the current on the black and blue wires, so the neutrals cannot be overloaded without tripping a breaker. If they're not wired anti-phase, however, the current on the neutral wire will be the sum of the currents on the black and blue wires. If devices on each circuit are drawing 20A, the current in the neutral wire will be 40A--dangerously overloaded.
There are too many unknowns here for us to help you out. We don't know which switches you intend to use afterwards (locations), what access you have to joining the circuits together, or what the possibilities of joining them would be without knowing of your personal setup.
Your setup, roughly as described to us is...
<--- S --- S --- Kitchen Lights
<--- S --- S --- S --- Adjoining Room Lights
The arrows (<---) would be your final wire running back to the source. The (S)s are your switches. And the (---) are wires between each. Now, this doesn't have to be physically wired in this setup nor does it have to be the only load on the circuit (no outlets or anything else?), but it would be how things are internally wired to control the lights. So no matter where the power actually comes in or where the switches are located in relation to the lights, this will be how the connections are made.
Then, if there is nothing else being fed from the kitchen circuit and you're intending to use only the 'adjoining room switches', you could simply disconnect and remove the breaker, wiring, and switches feeding the kitchen lights. Find the first light in the kitchen in sequence that receives power from the switch and add a wire between it and the power feeding the 'adjoining room' lights. The easiest way would be if you can get above the lighting, such as up in your attic, but where ever is accessible will work. Reconnect the hots, neutrals, and grounds and you should not be able to control all of the lights from those three switches. Your new layout would look like...
<--- S --- S --- S --- Adjoining Room Lights --- Kitchen Lights
However, again, this goes off of the assumption that you're fine with controlling them all from just the adjoining room location. If you're hoping to split the switches up between the kitchen and that room; then it'll all come down to how everything is currently wired, which switches you want to use and which to remove, and what wires are ran between each and from where. To get a complete answer, we would need a lot of information. However, a licensed electrician would be able to figure this all out on his own and get the job done for you.
Lastly, as I've had to mention recently in another post, four way switches are only used between two three way switches. You might have a four way switch setup in the adjoining room, but that does not mean that all three switches are four ways - two are three ways and only one would be a four way.
Best Answer
You are using the conduit wiring method with THHN wires*. In this wiring method,
That's not news to you. This is: NO SUBSTITUTIONS. In things like switch loops and 3-way circuits, you often see a white wire used as a "hot". They're supposed to be marked with tape but nobody does. This is only allowed in cable wiring methods where you have no choice of wire color. Not here! In conduit with THHN, you must pull the correct color, period.** You can mark them with tape, but doing so can't turn a neutral to a hot.
Another thing about conduit is the new "neutral in a switch loop" rule does not apply. That's because it's easy to pull a neutral wire in the future. Switch loops will have always-hot and switched-hot.
One rule remains the same: Currents must be equal among all wires in a cable or conduit. This could also be called the "Tree rule": circuits can branch but one branch can't loop back to rejoin another.
A side-effect of this rule is neutrals are not promiscuous: A neutral can only be a neutral for the circuit it's part of. For instance you cannot use the lower-left white wire to provide neutral for the upper-right black wire; they are on different circuits and this will result in unequal currents in both conduits, as well as overload the neutral. Neutrals don't have circuit breakers! Their only protection is honest wiring: If a neutral returned two circuits' worth of power, it would overload.
Any promiscuous/stolen neutral issue will also trip a GFCI protecting the circuit.
To answer your questions briefly, #1 if it's white, it's neutral for the accompanying circuit only. #2 That's just phantom voltage from running parallel to the hot wire. Don't worry about it. #3 NO because that would involve stealing neutral and violating the "equal currents" rule.
So on to your problem. Let's divide and conquer.
The top right "circuit"
Current can't return from a load without a neutral. And currents must be equal in each conduit. And there's no neutral in the upper right conduit. That means it can only be one thing: A switch loop. You confirmed this in comments. A switch goes there.
I imagine the red and black went to the two conductor screws on one switch. This is the only possibility without violating the "equal currents" rule, so it must be so. If you feel the switch is useless to you, you can create an "always off" switch by capping both wires separately -- or an "always-on" switch by tying both wires together with a wirenut. That would free up one yoke space in this box, for say a receptacle.
You cannot alter this circuit without a lot more analysis and work. Next.
The left "circuit"
Reds went to the switch, whites nutted together. Straightforward stuff.
If you wanted to fork a receptacle off this, make 3 6" pigtails: 1 white and 2 red, from #12 THHN stranded wire. The receptacle gets 1 white and 1 red pigtail. The switch gets 1 red pigtail on 1 switch terminal, the other terminal goes to the red from the upper left conduit. Now tie all the whites with a wirenut, and all the dangling reds with a wirenut. Voila.
(This bundling by color is lucky, it's not a sure thing and can differ in different circuits.)
* Conduit in residential is unusual. Chicago requires it, mixed-use developments probably require it, large multi-unit buildings, or your electrician is picky! I've seen Romex Kaisers fill conduit with only black, white and red THHN, thinking they must follow the exact same color code as cable, but those fools would pull black+white for a switch loop (illegal obviously) and that didn't happen here.
** Except in very large sizes, 4 AWG and larger, generally used as feeder or service.