1) wow, that is quite the stretched chain! and resulting shark-finned teeth on the small chainring. I take it the large chainring was less-worn and works fine with the new chain?
2) I can't confidently tell if the chainring pictured is a 38t or 39t, but am confident it's not 42t (the other common small chainring on a road bike). It's most likely 39 because that's much more common than 38. Plus you recall it was more than 38t.
3) It appears that your large chainring doesn't have pins/ramps/gates to aid shifting, and so it's less important to match it perfectly to a certain designation of small chainring. You'll be fine with the 38.