My old 1912 14" was also inspected by "JS"
my serial # was 352.55 putting your machine somewhere between 1912 and 1915.
The broken bolt is trivial, it is the carriage lock screw which pulls up a hold-down plate onto the underside of the way to bind the carriage. You may have to take the carriage/apron off to get to that stuff but the hold down is a simple piece of plate, drilled and tapped.
Compound screw and slide lubrication is oft neglected, so that whole assembly may be very gummed up. If you can withdraw that taper gib from the compound that might help a lot- but don't force it, that tang can break off if you put a lot of pull from the adjustment screw. Later designs put a couple ball oilers on either side of the compound to assist lubrication of the slides, likewise ignored... but at least on those its easier to get oil into the slide lol
ATW liked to secure parts with taper pins and bolts, eg the leadscrew support- I assume the knuckle-draggers have been in before you so some empty holes like that should have taper pins in them. Gits oilers are easily fit to the empty holes that are intended for lubrication instead
IIRC my old 14" had 32 holes needing gits, but it was a gearhead. Link below;
American Tool Works 14" Lathe
I went through it in some detail, so some of the pics might be helpful. Yours looks like its in better condition than mine was, but I did get a lot of productive use out of mine & learned a bunch. It was pretty beaten up though, I later upgraded to a 1936 ATW 12" which is in the shop now- and is in very much better shape.
Greg