Random bit of pipe as a damage shield
TLDR: any pipe or bent metal will do, and conduit rules don't apply.
If you are just using a stick of conduit here and there as a damage shield for the area that is low on the wall, then any piece of metal will do - you don't need to use conduit or even think of it as conduit. (old gas pipe? 2x4 with a slot in it?) As long as the cable physically fits, that qualifies. You can come down to a junction box and use conduit fittings to get the (iron water pipe?) into the junction box. The top of the pipe doesn't need any fittings at all, but you must de-burr the pipe, which your wedge-shaped multi-tool is designed to do.
My go-to for that is a $1.00 "4x4" junction box with a 99 cent domed cover for 1 or 2 receptacles. You can bring in any threaded pipe by using 2 conduit nuts back to back. I enter that with EMT thin-wall metal um yeah, conduit with a coupler, because it's great protection and it's low profile. Also I have loads of it lying around lol. Since you're not using it as conduit per se, there are no conduit fill rules other than "don't damage the wire". 10/3 NM can be crammed into 1/2" trade size conduit if the 10/3 is round. If it's flat, you'll need at least 3/4".
Conduit as a full-and-proper wiring method
On the other hand, if you were running conduit as a wiring system...
Presuming that you are running the entire run in conduit, which is a great system...
Remember -- you MUST build the conduit EMPTY and then pull the wires into it after the conduit is completed. If that is making you nervous, then you might be planning the conduit incorrectly. Access points must remain accessible forever. Curves must be sweeps unless they are a "conduit body" or junction box with an access cover. Splices require larger junction boxes not conduit bodies.
Harper's rule: buy the wire LAST. It's best to wait until as late as possible to buy wires, so you benefit from more collected knowledge. I.E. build the conduit before you buy wire.
In fact, check with your buddy - who may have big spools of this wire far cheaper than the "short spool" or by-the-foot prices nearby, and in more colors.
With THHN wire, your ideal selection is:
- two #10 black
- one #10 white
- one #10 green or bare
- one #12 blue (can be red or black)
- one #12 gray (can be white)
You only need one ground wire which both circuits can share.
On the 240V circuit, both "hot" wires should be the same color IMO. There is no useful use to using red & black here, because there's no value in distinguishing the phases. You are much better off using black-black, so if later you want a second 240V circuit in the pipe, you can use red-red.
The 20A circuit is also allowed to use #10 wire, but you really would need unique wire colors at that point, or a good method of wrapping with tape to identify conductors. (shrink tube being ideal). Tape and labels tend to fall off.
You are allowed to tape white wires in conduit - this does not change them from neutral to hot wires.
As things are, you can use black and white #12 and "get by on feel", but if you have gray and another color available, I'd say "use it".