Omega ref. 2271.1 35mm Cal. 265 Hand Wind

This is a new watch for me, that was just returned from the watchmaker. Running terrific. I do have some questions, and am hoping some of the experienced hawkeyes will weigh in. While being serviced the mainspring and crystal were replaced. Was Omega even putting the symbol in the crystals in 1949-50? I also suspect that the signed crown is a retrofit, and if so I am not really concerned with replacing it. The bracelet is an inexpensive one that I shaved the endpieces down a hair to fit. My bigger question is the dial, to my amateur eye is seems OK, but there is so much I do not know.
I have scratched a number of my expected Omega itches, and now I wish to turn my attention to what I consider the somewhat earlier models...this being my first effort. I want to get an extract to determine the exact date of manufacture, but have never got an answer to a couple of inquiries from the Omega site. There is not an AD where I live. This particular item is what I consider a "fun watch", and total authenticity isn't critical. I do expect I will be more careful with future acquisitions from this and earlier eras.

Case diameter: 35.30 mm
Case thickness w/o crystal: 7.70 mm
Watch depth w/crystal: 10.55 mm
Crystal diameter installed: 30.85 mm
Lug width: 17.70 mm
Lug-to-Lug: 39.90 mm
Crown diameter: 5.30 mm