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.

Splitting the hots and sharing the neutrals like that is no big deal; this is called a multi-wire branch circuit (MWBC). We have several answers on that, and Google can help too.

MWBCs are perfectly reasonable and safe. They are a little confusing at first, but they are good at delivering twice the amount of power with only one more wire.

Because if the shared neutral, a few extra installation rules apply. Most especially, make sure the hots are on separate poles. That is to say, there must be 240V between the two hots. Just use a 240V breaker, of the type which takes two breaker spaces, and requires both sides be turned off together.

A 30A breaker on 12 AWG wire is not allowed. You need to downgrade the breaker to 20A.

Any circuit breaker supplying 15A or 20A receptacles must be no larger than 20A, so the 30A breaker would not be allowed even if the wire was thick enough.

If you really, really want to decommission the MWBC and turn it into a single 120V circuit, you can do that. Just disconnect and tape off the red wire in the panel, put the black wire into a 120V breaker of appropriate amperage (i.e. 20A), and move the wires so that everything feeds off the black wire instead of the red. Honestly this seems like a foolish thing to do, it would be smarter and faster to just school up on MWBCs so you feel comfortable with them.

Edit: so you're out of spaces. As I said in the comment, you can join 2 circuits to become 2 branches of 1 circuit, and make that join right in the panel 6" before the breaker (or at the breaker if it's listed for 2 wires).

You can also do that with MWBCs - just land both hots on a single-pole breaker sized for one wire (e.g. for a #12 MWBC, a 20A breaker, not 40.) Yes, you have the dangerous condition of both hots being on the same pole, but the breaker is sized to protect the neutral, so it's not dangerous.

Lastly, you say the MWBC backbone is actually 10AWG. (heh, former dryer circuit). That veritably screams "put a subpanel at the end of me". That would support four receptacle circuits, and easy with 10AWG - no wrestling black snakes. Breaker the main for 30A to protect the 10AWG wire (the subpanel can be anything >=30A). If the MWBC splits there, land each side on a single. Otherwise continue the MWBC off a 2-pole. Now you have headroom in that panel for 2 more circuits. More if you ever upgrade the 10AWG backbone.

I strongly encourage you to be "once bitten twice shy" about running out of breaker spaces, and get the biggest panels you can, always. I joke about 84-space panels, but panels get expensive once they exceed 40/42-space, so just get two 42's :) By the way, industrial quality panels always have multiples of six because they also come in 3-phase -- therefore, 16 or 40-space screams "cheap builder-grade panel type".