I had no idea that it wasn't a round post. The only similar vintage Cannondale I own is a 2011 CAADX and it has a round post. Looking at the catalog it appears that the aluminum Synapses had round posts.
If you're going to repaint, I would go with whatever color you like. I doubt that a non original color would hurt the value very much, and we see colors all the time that don't show in the catalogs.
It's a CAAD 3 from the late 90s, so likely an F1000 or F2000. Check out the catalogs and see if any of the components match. Could be a team frame if the sponsor decals are under the clear coat.
3X is for the triple crank. Sora was a fairly low end parts group, usually on R300s. Looks to be a CAAD4 frame. I would check eBay sales of R300s/R400s. Facebook, Craigslist, eBay are probably the best places to sell.
I think that the M192 is the front derailleur. My guess is you have an Altus M370 rear. Check the back of the derailleur for a model number.
I would check Wheels Manufacturing for a replacement hanger.
https://wheelsmfg.com/derailleur-hangers/manufacturers/cannondale.html
I think the A in the CAAD2 decal is supposed to be interpreted as two A's, with a smaller one inside the larger one. Substitutions to catalog spec were fairly common for Cannondale.
Circa 2001, looks to be size 50. See how the geometry of your frame compares to the 50 in the chart. I think there was a 50 feminine in 2001, but the scan we have is virtually unreadable.
Only the SM800 shows in the 1991 catalog as being jade green, but that could be a replacement frame or sold as a frameset. It's not an SM800 as they had a sloping top tube. It has 26" wheels? Steel fork? That would make it SM700 or below. Check the component lists in the catalog and see if...
Wheels needs to work on their Cannondale model list. There's nothing there before the CAAD era but they list that hanger as fitting 1991 frames. There were no CAAD frames until the 1996 hybrid and MTB frames and 1997 for road frames.
Is that a 20" frame or a 22"? I have the same frame and fork here, 22" frame. If I ever get around to packing it, it's probably headed to Idaho Brett to build up. I think it would look great with a full 1993 Shimano LX build, as everything is black.
Since you need a new freewheel (not cassette) anyway, you might as well see if you can convert the bike to 7 speed. I'm assuming that you still have the original wheels. You will need to see if there's room for another cog. According to Sheldon Brown a Shimano 7 HG freewheel is only 2.4 mm...
I think the Wheels Mfr. #17 is the right one. I can pull one off a CAAD2 road frame and check it on a 3.0 but it will take me a while.
https://wheelsmfg.com/derailleur-hangers/manufacturers/cannondale/derailleur-hanger-17.html