Minimum receptacle spacing.
NEC Article 210.52(A)-(H) tells us that, the maximum distance (measured horizontally along the wall) to a receptacle should be no more than 6'. There are two important exceptions to this rule. doors, fire places, and other openings do not count as wall space. Also any wall less than 2' wide, does not count as wall space. The idea here is that if you have a lamp with a 6' cord, no matter where you put it (along the wall) you should always be able to plug it in.
Lets take this 20x20 room for example.
We'll need a minimum of 6 receptacles, in this room to meet code. You'll notice the wall with the door and closet, only has 1 receptacle. This is because the doors, and the 1' 11" wall between them do not count as wall space.
Keep in mind, however, this is a minimum code. You can always install more receptacles, if you want to.
Calculating loads
Once you've determined where your lights and receptacles will be placed, you'll have to determine how many and what size circuits you'll need. For this, we can reference NEC Article 220.
Lights
For dwelling units, we'll use 3 Volt-Amperes/ft² to figure out how much lighting we might want. When measuring area we must measure from outside to outside, so we'll have to include the wall thickness in our calculations.
So if we have a 20'x20' room, with 2x4 walls and 5/8" drywall on each side we'll get.
3 1/2" + 5/8" + 5/8" = 4 3/4"
20' + 4 3/4" = 244 3/4" = 20.4'
20.4' * 20.4' = 416.16 ft².
416.16 ft². * 3VA = 1248.48VA
We know that a 15A circuit will be 1800VA (15A * 120V = 1800VA), so we can see we'll only need one 15A circuit for lights.
Receptacles
When calculating loads for receptacles, we'll use 180VA per receptacle. Using this value, we can determine that we can have 10 receptacles on a 15A circuit.
15A * 120V = 1800VA
1800VA / 180VA = 10
For each 20A circuit, we can have 13 receptacles.
20A * 120 = 2400VA
2400VA / 180VA = 13.3333333333
It's a good idea when wiring up a new room, to keep the lights and receptacles on different circuits. This is not required, but it does make practical sense to do so if you can. As an example, lets say you have the lights and receptacles on the same circuit. Every time you vacuum the lights dim, then the breaker finally trips. Now you're left standing in a dark room, trying to get to the door without stubbing your toe. If the lights were on a separate circuit, you wouldn't stub your toe.
∴ lights + receptacles on same circuit = stubbed toes.
Now I'm not saying you should have a bunch of circuits with a single light on them, just that it's a good idea to have receptacles and lights on different circuits. You could always share a light circuit across a few rooms, to decrease the number of circuits required.
The best way to figure out how many, and what size circuits you need for a room. Is to plan out how many consumers you'll have first. Decide how many lights and receptacles you want, then determine what size/type of wiring you'll need.
EDITED FOR CLARIFICATION:
If this is wired as you have drawn it, then it will not be a safety issue. The additional neutral will only share the current in both circuits. Because both circuits are fused for 15A, each neutral will only see a maximum of 15A. This is providing that both neutrals are solidly connected! If one were to become loose or disconnected then the other can potential see the full load, 15A*2=30A.
If anything else is fed from either of those breakers, it becomes a whole other issue!
I recommend you wire it the right way. However to answer your question, I don't see it as a safety issue if that is the only circuit on those breakers.
With either breaker off, that circuit will be isolated from the energized circuit. The only common path between the two is the shared neutral. If the energized circuit were to draw the breaker maximum of 15A, the de-energized neutral potential would be at maximum only a few hundred millivolts, not posing a safety risk.
Also it is not against code to have more than one feed in a jbox or switch box.
Best Answer
Yes, you can -- just mind the box fill and labeling, and make sure to keep your neutrals separated!
A five gang box composed from gangable, 2¾" deep boxes as you describe provides 70in³ of fill (14in³/gang as per the Steel City catalog). You are bringing 4 14/3, 3 14/2, and 2 12/2 cables into the box, in addition to mounting five devices in it, three of which are connected to 14AWG wire and the other two connected to 12AWG wire.
This means that we are using 72¾in³ of fill; 36in³ for the 18 14AWG wires, 9in³ for the 4 12AWG wires, another 9in³ for the two receptacles, 12in³ for the lighting controls, and finally 6¾in³ for equipment grounding, as per the 2020 NEC rule that requires an extra equipment grounding allowance for every four additional ground wires past the initial allowance's worth. This is just a hair over what your box supplies, and would be legal under the 2017 NEC fill rules as the fill for the additional grounding wires is what pushes it over the top, but doesn't account for any cableclamps internal to the box. As a result, I would go with a 3½" deep box if you are sticking with the field-gangable boxes, or order in a factory-fabricated 5 gang box that is taller and thus provides more fill volume if you'd rather go that route.
You'll also want a consistent way of labeling your wires so that you can tell the various circuits involved here apart; crossing your streams could lead to false AFCI trips, overloaded neutrals, and other such badness. Thankfully, premade wire labeling booklets are available for this job, and make this relatively simple; all you have to do is come up with a consistent scheme for using them.
Finally, even if you don't use the wire labels, you must keep your neutrals on the two circuits separate for the reasons mentioned above. However, you also must join all the equipment grounding wires involved together and pigtail them off to the box and to the receptacles (unless they are self-grounding that is). (Think of how this'd turn out if you were wiring this in Chicago, where you'd have to use metal conduit instead of cables.) In fact, you could use a divider in your box between the three lighting controls and the two receptacle devices; you'd then need grounding pigtails in both compartments, but it would make it much easier to keep your circuits apart.