2) Is it OK to use 10 and 12 gauge wire on the same 20A receptacle circuit? The previous owner ran 10 everywhere and seems a waste to pitch it and run all new 12. What about using 12 for pigtails since 10 is a pain to get around screw terminals? (I know not to mix 14 and 12 on a 20A circuit.
Now I know why you said the wiring was mucked up. That 10 awg shouldn't be there...he must have had some free 10 from somewhere. If it were me I'd make some dedicated receptacle circuits with it for shop tools.
Yes you can pigtail it with 12 as long as you use a 20 amp breaker. Again if it were me I'd use the 10 to make a welder circuit with it and maybe single outlet space heating or fixed heating branch circuits maybe a few machine tool circuits. In other words use it where it makes sense.
The problem I have with what exists is it appears you have possibly 3 wire sizes with one general purpose branch circuit. Screw that!!! Makes you look like you need a stupid hat , the guy that did that sure did....
I can only tell you that cost savings only goes so far with me. I'd much rather have something that made sense and shows I knew what I was doing rather than wire that is a hundred miles overkill and out of place.
You mentioned one thing that caught my ear and that is you want a shop some day and you do not plan on finishing the garage. So this sorta gets us around to talking about the physical protection of the wiring since you have open wall stud cavities. So I just tell you if I wired this garage it would be either all EMT and thhn individual wires with metal device and fixture boxes or I'd drop from the joists or trusses with sleeves of EMT to the switches and receptacles running my cables in those protective sleeves.
At any rate back to your switch box. I'd wire it the way you want period. Wire is not that expensive. But if you notice there isn't any load amps involved with just that one light and even if the other light was on that circuit. After all everything is on one branch circuit correct??
So the simpliest thing would be to use the switch box as a jb and just splice to the power feed coming into that switch box for the outside light with a short piece of romex then down to a gfci receptacle for the outside. This doesn't get the lights on their own circuit but I really see no problem doing it that way.
Again though I'd almost think you should start from scatch use what wire you can that exists and get the 10 awg out of there or to special outlets as I mentioned before. Get the same size wire for your branch circuits ...14 awg for lights and 12 awg for receptacles (gfci protected) and wire it right....you will be much happier.
As for physical protection that is up to an inspector to decide but I can tell that many inspectors are going to require you to drop from the ceiling with a listed protective sleeve of some kind. That is almost always going to be EMT if I'm doing the job.
Best I can do, I just don't think I'm going to get any mileage out of trying to find easy ways to work with what exists. Others here will likely have suggestions so keep your screen tuned.....