Help me figure out what I have?

[Rolexette]

Hey there....

I have inherited this watch and I have a few questions after some online research of my own:

-How do I know the model?
- How do I know if it's a REAL Rolex? The tapered, fish skin-like band is faded a bit around the latch area. I thought there were none gold-plated Rolex ? It's missing the crown (the part that winds) so I can't check to see if it "ticks" or not.
- As far as I know, my mother-in-law got it from her husband as a gift in the 60's. Very unlikely one would be able to buy a fake back then, maybe?
- Is it worth fixing it? How much $ should I expect to spend?
- If it's a valuable watch, could someone give me a ballpark?

Thanks for any help!