Help Needed: Old Omega from my Grandfather

Hi everyone, watch lover here. Just been given this beauty that belonged to my grandfather and came across this forum whilst researching the watch and trying to figure out what model this is. Whilst I'm Portuguese and we always lived here, my Mum told me that the watch is likely to have been acquired in Brazil during one of his stays over there.
I thought I had pretty good searching skills but couldn't find a similar watch on the entire web. The closest I got in my research is the "Omega cal. 30t2", but it's just similar, not the same as this one has got all the numerals. The watch says it's 18k gold, and I can confirm the mesh is also made of gold as I took it to the local jeweller to get it cleaned but got told it would take at least a month. I was also told I would have to cut the mesh (my wrist is slim) if I wanted to get it to fit (or purchase a leather strap, which I declined). I intend to wear it as it is after it's ready.

I was inspecting it and I was surprised to notice it started to work! The watch has probably not worked for over 30 years. I've wounded it up and it worked straight away. Surprisingly, after 24H the time on the watch was still accurate. But sadly I also notice that it stops with some rather light movement, and when you gently tap the back or front it restarts.

The dial and the hands need cleaning, the crystal is scratched, and the crown looks a little bit rusty (perhaps it's not the original?

I know I probably have to get it serviced and I've got a lot of questions, as you can imagine, and wanted to ask if anyone had tips or leads, please.
A) As anyone got any leads or clues about what model this is? Does it look legit? I'm baffled I couldn't find it online.
B) Where would you get it serviced? At an Omega official store or to my local watch/jewellery store to be sent to a specialist?
C) Would you replace the crystal or would you leave it as it is?
D) I don't seem to be able to adjust the strap? Any idea how?

Any other tips and comments on this? Much appreciated in advance. Can't wait to wear it with pride knowing it was worn with passion and pride.
Many thanks in advance!
A

Thanks both. The bracelet is too large. I'll take it to a jeweller to open the case and will also record the movement without it the case, if possible.
Here's what it looks like from the front:
Thanks again.

This is fascinating, thanks for your reply. How did you come to the conclusion it's been repainted? on a closer inspection, I did see that some of the fill of the numbers do not reach the stroke. Would it have been hand painted? It would also make sense that the crown doesn't seem original either, right?

I'll try to get it open tomorrow before I fly back to London and try to see if there's any info on the inside and record a video of the movement.

How would your repair/service if it would be yours?
I think I will take @Dan S suggestion and get the bracelet cut once the watch has been "fixed".

After you see a couple thousand, it gets easier.

That made me laugh!
Another tell is the number 5 impedes on the subdial, which is not typically the case.

To answer some of your other questions

Do not send it to Omega - they will replace the "nice bits" and return it as a brand new watch. I can understand why they would do this but the charm will be gone.

Find an independent watchmaker, I could recommend a couple in the UK but no idea in Portugal

Leave the dial as is (my opinion). You could probably get it repainted again (and in all likelihood a better job too). But this is what your grandfather looked upon.

And best not to keep running it as you may do further damage to the movement.

Thanks for your advice. Will do. I'm based in London, so any tips welcome, please.

That's a great point, it just needs cleaning, for now.

I'm really curious to get it open and check the movement to confirm it's an original as being repainted and not finding anything like it is raising some doubts. After @ConElPueblo mentioning it could have been made in Brazil, I did a search in Portuguese and found a strikingly similar watch (attached here), but still nothing like like mine, sadly. Perhaps whoever got it painted used some more creativity?

Yes Omega have done this back in the day to prevent import taxes for complete solid gold watches one of the reasons why in US 14k Omegas are common but not in Swiss.

Firstly, thanks to everyone who's given their input and insight on this thread. I really appreciate it.

I didn't manage to get it open but I'm coming back to London today and will try to get this done this weekend at some point. I'll share the pics and video as soon as I manage to do so.

@ConElPueblo @shaun hk Can you recommend any trustworthy places in London, please? I can be patient, just so excited to get it serviced and on my wrist!

According to Mum, the last time he was in Brasil was late 60s/early 70s, and there's a chance the watch might have been purchased directly to someone rather than at a shop.

Update: I've been to 6 watch stores (including Ernest Jones, Omega and Watches of Switzerland) and none removed cases. The gentleman at the Omega shop told me to visit SOMLO at the Burlington Arcade in London, which is what I will do when I get a chance. If anyone has got other suggestions please let me know. Thanks.