Well, our electrician recommended Panasonic (apparently they are the most quiet) so we already installed the fan, but your suggestion inspired me to look for different Panasonic models and while doing that, I ran into this grille accessory, which looks a lot more attractive than what we have now. So thanks for helping out. Here is a link that might be useful: Panasonic vent fan antique grille

It's possible to get replacement bare motors sometimes. Broan are good about having replacement bases -fan/motor, that fit into the existing box. They have a plug/socket, so you don't have to do any wiring. That being said, I just replaced one, and it turned into quite a big job because the replacement base was more than a whole new unit. I put in a new one, which meant a bit of carpentry etc because the boxes were different sizes. I had to cut the nails/screws holding the old one in, and insert the new box from below, which required a bigger hole, and careful saw cuts in addition to allow for the nailing tabs. The fan cover covers the repairs from it, in the ceiling. The insulation around the duct had no vapour/air barrier so I used a mylar bubblewrap product and foil tape for it. Since the house was old enough to not have had an vapour bag around it, I built one with the mylar stuff and sprayfoamed it in. Lastly I decided the fan should have its own switch, so I could use one of those timer/humidity sensing ones. It turned out well and I'm glad I did it, it works better and is much quieter. But in most cases, just replace the fan motor and base.

This can vary a lot, depending on what the ducting behind your existing fen looks like, and how nearby there is electrical. The fan can be purchased at a big box or Amazon, and then it's just a matter of electrical... I bought a timer switch for mine, so that you could just push a button to have it run for 30/45/60 minutes and shut off. But it's all going to depend on where your electrical and duct runs are.

+1 on leave the toilet room exhaust. That is historically what exhaust was only required for. Now, code has updated wording to include "bathrooms," but doesn't talk about humidity (yet). HVI has more in-depth recommendations for bathroom exhaust and ventilation. You can only combine ducts if you are pulling the exhaust from 1 attic/roof sourced fan. When you are pushing the exhaust from ceiling sourced fans, you need to keep 2 separate ducts with each their own discharge. You have options for the shower. Based on the finishes I see in the pic and thus the level of bathroom, a combo recessed light/vent inside the shower footprint might fit well. Or a light inside, with exhaust/heater outside the footprint. With a combo light/exhaust/heater, it will all be moved just outside the shower footprint, so make sure you're fine aesthetically with that next to the old ceiling fan light outlet - I'd guess you will be putting a chandelier there. And don't have the shower light switched to any of the same switches as the chandelier, toilet, or vanity lights.