Wiring methods
EMT and other fixed metal conduit works as a grounding path, so you only need ground wire where the conduit is otherwise. Green, green/yellow or bare is allowed for ground wire. You don't need a ground wire per circuit, only per conduit, but it must be large enough for the largest circuit present. If bare, it must be copper outdoors.
You join a ground wire to EMT by getting a #10-32 screw and fitting it in the pre-threaded hole in the junction box. Do not use a sheet metal screw.
Conduit outdoors in conduit is outdoors. It's pretty much a foregone conclusion that your conduit will fill with water at times no matter how much you try to seal it... that's why you use THWN wire. It's designed to soak.
I have no earthly idea why someone would use solid wire in conduit, perhaps because they were buying (cheaper?) receptacles and switches not listed for stranded wire, or because they were a Romex Kaiser**. It's not worth "fixing", but I wouldn't do any more of it. It's fine for them to mix, just make sure your devices are listed to take stranded wire, and notably backstabs are not, but those are unreliable in any case.
Stranded wire costs about 5% more here. After your first time wrestling 6 solid wires and a GFCI into a 22cu.in. box, you won't mind paying 5% more.
Pulling
You have a tough pull due to the four bends, so gear up for a big one. THWN-2 is already pretty slick and lube won't be worth the unbelievable mess IMO.
The main way to prevent damage is first to thoroughly de-burr, and second prevent kinking, by watching the wires as they enter.
You cannot splice inside the conduit body. Out of the question.*
Pulling one wire at a time isn't better, it's worse. The big hank of wires will mutually help each other as well as provide added strength, whereas pulled individually the existing wires will drag on the new. Don't tape them mid-run, they need to slide a bit to go around corners.
Similar circuits
Beware of NEC 225.30, which generally prohibits running two similar circuits to a building. So having two unswitched 120VAC circuits may be disallowed. However 225.30(D) considers them dissimilar if they are switched, or a different voltage (240V). So the quickest way to clear 225.30 is put one of the circuits on a switch for some reason. Nowhere in the code does it require you to use the switch.
Marking wires
Tape is the key to marking when you don't have 8 colors of wire.
Don't distinguish wires unnecessarily: for instance the two hots going to a 240V heater or 120/240 dryer don't really need to be distinguished from each other.
In your case you need to distinguish two hots from each other, and two neutrals from each other (why? Because you might put a GFCI on one), and potentially a third spare hot.
You can put any tape color on any wire color, but it doesn't always do what you want:
Same-color tape is a little subtle, but is useful for marking. With colored tape it usually doesn't quite match the color or finish of the wire, and you can feel it.
In cable, it's easy to tell which wires are partner to a white, since they emerge from the same cable. This can drive you crazy in conduit with 4 whites coming out of a conduit. In conduit, remarking whites to a hot is disallowed (in most cases) but this cuts both ways: you can use the colored tape to distinguish different wires.
* To be pedantic about it, Code says any box/body is only a conduit body until you splice in it, then, it's a junction box... and must use junction box fill rules. This makes them way too small to splice in, in practical application. Even if the conduit body is wildly oversized for the wire, making the splice strangles the remaining capacity of the conduit, defeating the purpose "room for expansion" to oversize.
Now to be super, duper, duper pedantic, literally NEC says conduit bodies use conduit rules, but they have anything but thru wires, they are still conduit bodies but have to use special fill rules that are identical to the junction-box fill rules. And then, junction boxes use junction box rules, unless they have nothing but thru wires, then they are still junction boxes but use special rules that are identical to the conduit body rules.
** you can tell when conduit work was done by someone used to working in Romex, because they stay as close to Romex practice as possible, e.g. choose only black, white and red for the wires, and occasionally use a white for a switch loop. The old WWI German flag colors. Add green and you have the Pan-Arab colors LOL.
Best Answer
Solid vs stranded
A lot of people who work 99% in Romex find themselves gravitating toward solid wire because "it's the devil they know", they have no idea the difference, and they fret about terminations.
I work 99% in conduit and stranded is the only way to go. When you have a solid wire in the bundle (I'm cheap, I reuse wire). you know it and it's a fighter. As far as terminations, they're a little more finicky sometimes, but it's not a big deal. If one is out of your comfort zone, pigtail a bit of solid wire (wire nut splices solid-stranded are just fine). You want to be in stranded. Seriously.
#10 is the breakover above which all wire must be stranded. As such, #10 solid is a black swan - nobody who does conduit for a living wants to pull it, and so it is relegated to a specialty item. What's more, every termination meant to take #10 (eg NEMA x-30 receptacles) is designed for stranded wire.
We generally advise people to underfill conduit to keep the effort of pulling easy. That's why we'd tell you to use 2" conduit for three #2’s. Otherwise you could run out of swear words and have to call the guy with a truck full of pulling tools, and he probably won't want to come in for just the pull. Since you are near conduit fill limits, you should expect a challenging pull. If you attempt this with solid wire, you should expect a very, very challenging pull.
You may be tempted to dismantle the conduit and reassemble it around the pulled wire. That is not allowed, and will work particularly badly with solid wire.
Conduit fill
RME describes the gory details and the source material. I just google "conduit fill calculator" and pick one I like. One that lets me state # of wires of each size, and does the lookups for me.
For conduit fill (NOT derate), neutrals and grounds count, as do for instance fiber optic lines or Class II wiring, since they all take space.
Solid vs stranded doesn't matter, the slightly larger size of stranded is a "gimme". There are a lot of gimme's in fill calcs, wait til you get into junction boxes!
You're fine, but you are also essentially full.
Conduit wire derate
This won't affect you because you are full.
Too many wires in one conduit will get too hot (you're a long way from this problem). In residential/split phase, each circuit can only have 2 conductors because like I said, neutrals and grounds don't count. But even if you were doing something odd (lopsided hot/neutral on 3rd circuit? Two 3-phase delta circuits?) it matters not: 4-6 wires have the same derate. 310.15(b)(7).
Look up any wire ampacity chart [called 310.15(b)(16)] and note the top row, which calls out which wires each column applies to. THHN and THWN-2 use the 90C column. If you happen to have an odd duck called THWN (obsoleted by THWN-2), that uses the 75C column. Follow those down to your wire size. That is the point we derate from: example is 40A for #10 copper THHN.
With 4-6 wires we derate 80%. So #10 THHN derates to 32A. #12 THHN derates to 24A. That puts you in the clear with both wire sizes, since you are already capped at 30A and 20A respectively due to other Codes (240.4).
Generally you can have 3 single/split phase circuits in 15, 20 or 30A without even thinking about it, and 4 if they are all 15-20A. Larger than that, you have to break out the sharp pencil, as above.