Boilers that are well maintained should last a lot longer than 25 years. If there is nothing wrong with the boiler then I suggest replacing the gas valve and the low water cut off and use the boiler for another 25 years.

How was the size of the new boiler calculated? Did the contractor measure the size of each radiator? How does the new size compare to the old size?

No he didn't measure our radiators . I think he gave us his quote based on the same BTU as our current boiler
In any case , we are going to suck it up and do the repairs first just because we can't afford to do the new boiler right this moment. We are already spending more than we anticipated for the repairs since an electrician had to get involved as well. Something about the plumber not being familiar with "boiler circuitry" . That already gave us strange vibes since we had no idea we would need to pay for service of an electrician on a part a plumber was supposed to repair!
The plumber also showed us (as indicated in attached pic) a leak that has been going on. Not sure if we should be worried about that as well ?!

You need to hire a steam heating contractor and not a plumber. This guy does not seem to know what he is doing.