Questions about my '60s Constellation

[RFP]

I have owned this '60s Constellation for several years, but up until I took my Sea Dweller in for service, it didn't get much (any?) wrist time. Too bad... after wearing it for a few weeks I really, really like it (although it is pretty 'dainty' as compared to the SD).

What I know about the watch isn't much... this is pretty much it:
Stainless case does not appear to have ever been polished, the angles and 'edges' are nice and crisp.
The "Omega" script, the omega symbol, and the little star are all applied on the dial.
The crystal is new... I had Kevin at TimeTech (in Dallas) completely service the watch when I got it)... it has a little "omega" symbol in the center of the crystal.

There's a lot that I don't know, including...
How can I tell if the dial has been refinished?
Does it have the correct crown?
What movement would be in this watch?

I would be most grateful for any 'answers, that anyone could provide!

All the best,

Rob

PS: This thing keeps excellent time!!