Old Omega Geneve - Authentic? Worth reparing?

It looks authentic, the reference number is inside the case-back. I think that maybe someone damaged the dial attempting to re-attach the dial feet. Because of that damage, there's really not much you can do to improve it.

Looks a bit rough. Dots on the dial? I suspect the dial feet (hold the dial from underneath) may have broken off at one point, and some sharp operator drilled holes through the dial in order to patch the broken feet! Externally, the watch looks rough, and I suspect it will be rough internally, also. Before you spend 10¢ on the watch, it would be smart to gather opinions on how much life remains in the bracelet. If it is as rough as the watch appears to be, it will be difficult/impossible to replace, and you have no options as to a generic replacement because of the case design. As to “is it worth restoration”? You have much fact gathering to do before you have a price to consider. After that, it is up to you as to whether it is worth it. Better examples are likely available that don’t require major intervention than what the subject watch does.

That dial makes this a bit rough here. As others have said those are the dial feet someone has glued on. They would bother the crap out of me, and I'd want to replace the dial.

If the bracelet is pretty worn out, wearing this on leather is not a bad idea.

That said, this is not a particularly valuable model, so you'll be spending about its value on a movement service (let alone any amount of restoration/replacement dial/etc). You'd probably be looking at a minimum of about $500 to fix it (~$300 for a service, then another $200 for a dial + crystal swap). IF this doesn't have sentimental value that makes it worth it... well, that would answer that question 😀

It's not easy to wear this model on a leather strap.

Ah shucks, I missed the reduced width 'tang' there. So you'd probably need something custom, which is ~$100 for a leather strap, though most etsy sellers will make it for you.