Electrical – Running conduit from an old rectangular 2 x 3 exterior box

For conduit fill calculations you have to treat romex/NM as a ROUND wire of the same size as its largest dimension (ie, the long axis of the oval.) Oddly enough this means that 14-2 is larger than 14-3 for conduit fill. As @SpeedyPetey notes nipple (less than 24") fill is 60%, not 40%, and is a LOT of wire to get into a conduit; but I don't think that's the major issue here if NEC compliance is a desired upgrade. The wire type and location is the main issue.

NM cannot be run in exterior/underground conduit since it is not rated for wet locations. With an outside service box that alone might mean you can't do this and meet code - at which point you'll need a major junction box or a lot of minor junction boxes inside, and some wet-location-rated wire until you are inside.

(And now that I've seen the pictures...)

My understanding of NEC (which does not seem to have been particularly involved in your current service, with exposed NM running outside) is that you would have to run a wet-rated wire (THW, XHHW, etc.) until you get inside the house, where you would connect to the interior type wire you currently have exposed to weather and sunlight. NEC defines (and reality frequently confirms) all exterior conduit as a wet location.

"In the way of a stud" implies a heck of a lot more stud consistency than is actually required in a (pretty clearly) non-load-bearing wall, for one thing. But if you feel you must, if there's no wire into the wall from that box, you can reposition the box by pulling out the wire, cutting the conduit and using a conduit coupling to shift the position of the box along the conduit by the amount you cut off. Of course, at that point you need new wires on whichever side got longer in that event, since you would otherwise need an accessible junction box where the box you want to move was.

NM cable is generally not allowed in commercial, for another.

And junction boxes cannot be covered up, period. They can, however, be extended to the face of the wall (look at box extension rings, they clip to the box like a cover at one end, and take the box cover at the other end. Alternatively, there are standard access panels to install in drywall and give more working room (if the wires won't come out to the face of an extended box, you once again need new longer wires that will. A panel makes the original non-extended box accessible.)

Personally, I'd suggest getting comfortable with bending EMT - it's not hard, and it's got some advantages over MC in my opinion (you can pull wires as needed, for the most obvious point.) MC may be an easier concept if you think like NM but need to work commercial, but in many cases EMT will also come out cheaper all told.