Converting road single speed bike to 1x I have a very nice bike that I built from a vintage new steel frame, threadless bottom bracket (because of the french thread in the frame) and 110BCD crankset. It is currently mounted as single speed, and I would like to add a rear derailleur.

The dropout spread is 125mm and the current chainline measurement is 45mm.

I have many questions and try to evaluate the feasibility. I would like to keep as many parts as possible, in particular not change the bottom bracket because of the odd standard (and the fact the thread is in part damaged).

I am contemplating the SRAM 1x solutions, but I don't know if 11 speed compatible wheels will fit the 125mm dropouts. 

I suppose I could pick a 9 or 10 speed wheel (would they fit?), and add a 9 or 10 speed rear derailleur, but I am not sure of the chain line that is required.
Steel frame can be set out to accommodate a 135 mm rear hub without substantial effort (bear in mind that the dropouts will need to be realigned).
With a rear derailleur the chainline is not an issue (in my opinion) as long as it is not kept on the most outside cogs in the rear.

You can also play with the chainline by mounting another crankset (different offset) or changing the bottom bracket spindle (you mention that it is threadless, you don't say which type is it exactly, cartridge bearings vs cup and cone).

What is often an issue in such conversion (I personally dropped one frame and kept it as fixie because of that) is whether all the derailleur cable eyelets and shifter bosses are available. Also you'd need the derailleur hanger or a suitable adapter.

Have you considered internal gearing hubs? There are Sturmey-Archer or Shimano models widely available with up to 8 gears if I'm not mistaken.