My Dad's Constellation Pie-Pan

Dear Omega Forum,
This is my first post. I present you a watch whose history I know very well.
My dad bought this watch brand new in 1963 for his wedding to my mom. I was born a year later 😀
My dad purchased the watch from an authorized Omega dealer in Caracas, Venezuela. At the time, Venezuela was the hub for commerce in Latin America. This was his favorite watch, and when he passed away, it was the only thing I really wanted from him. I remember wearing it as a kid and being fascinated by it. I had many conversations about watches with my dad, which ignited my appreciation for horology and my hobby of watch-collecting.

I have two questions for you:

1) I am intrigued that the dial does not say "Swiss Made." I have read that some genuine watches did not have that inscription on the dial, but I remain curious because I know my dad never had the dial replaced. The only time I remember the watch getting serviced was in the mid-1980s, in Miami, FL, but as far as I know, he did not swap out any parts. I do think the crown was replaced at some point because it has a round crown. What do you make of this?

2) I would like to change the glass and the gaskets for the case back. Which parts do I need? Where to get them from?

The caliber is: 561 The case is stainless steel, model: 168.005 (All this as far as I know)

The watch is running great and keeps good time. As you can imagine, it is priceless to me.
Any other advice is much appreciated. I am enjoying reading all the great stories on this forum. Nice group of people.

Thank you, @Zman4eva and @Davidt, for your observations and ideas. I am surprised that someone talked my dad into repainting the dial. Perhaps, as you say, at the time, there weren't many resources to educate yourself and make the best decision.

If you, or anyone else, know of an excellent place to source parts, like the gaskets and glass, it would be much appreciated. It is one of those things where I don't trust Google so much.

Cheers!