You need to take it to a watchmaker to open the case as the case reference will be on the inside of the back. Take a clear photo of that and the movement.
As it obviously has lots of sentimental value you should get it serviced by a reputable independent watchmaker if you want to wear it. Even if it runs ok the oils will be dry and the parts will get worn out and replacement parts are expensive.
To me it looks like it has a bumper movement like a cal. 354. You're right in thinking it is gold capped as opposed to solid gold. At some point the dial has been repainted.The crown and hands look correct and you should check to see if the crystal has a very small Omega logo etched into it in the centre.
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