An amateurs questions about half-working vintage Omega

Most likely an issue with the setting lever or the pressure spring that holds it in place. Not sure the stem is correct for an automatic. These often have a clearance for the rotor.

As for the reference one would have to open the back to read the numbers. There is not enough info to tell if this is a rotor or a bumper.

500USD seems a reasonable price. The whole movement will need a good service. The crystal scratches can probably be polished out. Never buff or polish the case.

The spandy strap could damage the lugs. These look best on leather.

I agree with @sheepdoll . Also, the crown is a generic replacement. Any watchmaker with an Omega parts account can source a genuine Omega replacement crown, but it won't be what was on the watch originally. An original crown can be sourced with a little effort. To do that you will need the reference number which is on the inside of the caseback. In spite of the name Seamaster, the watch is not and never had much water resistance. So be careful not to get it wet.

If you plan to wear the watch, I would get a full service which should sort out the issue with the crown and steam. If the $500 repair price includes a full service and he/she is a respected watchmaker I would go for it. I would expect to pay my watchmaker more like $800 to get this done, but I don't go to him because he has the lowest price.