If you want to destroy the dial, then go ahead. If you want it to be done professionally, find a watchmaker.
Do not attempt to relume the missing lume on dial, new lume has different colour tone comparing to those aged lume dot. Trust me, you won't like it.
As for the crystal, if you can "push" a crystal in with your bare hands, your crystal may be not the right size. Often this is done with a watch crystal press.
And FYI, if it's original plexi glass and tension ring, I'd suggest you to leave it alone. Because you have a very high chance of breaking it when removing the crystal because the tension ring is so freaking tight.
Original signed plexi is hard to find and expensive
I have ordered a crystal press from ebay, but my watchmaker said that a regular crystal without the edge wouldn´t be possible to mount on that watch. Is he right about that?
TBH, I don't think you need a new crystal, the crystal look good to me, just buy a Polywatch (crystal polisher) rub it circularly with micro fiber cloth for 10 to 15 minutes, your crystal will be good like new.
And your watchmaker is right, original signed crystal's design is unique and extremely hard to find. Just polish the crystal, it will save you from a lot of troubles.
Not that because you have a watch press, you would be successfully pressing in the crystal, it require skill and experience, a slightly misplace or unbalance will led to breaking your crystal
The Universal Geneve Polerouter website has a couple of sellers selling NOS crystals which are signed but they are fairly expensive. If okay with compatible but not signed crystals ebay is your best bet. I myself am looking for a NOS signed crystal at an affordable rate. I'm sure one will pop up if I'm patient.
The watch hasn´t any crystal at all. You look stright into the dial. It´s not an ordinary watch press I´ve ordered but something like the picture here: