Hi Andrea,
I will share my experiences in Rome around the date of December 8th.
As you noted, it is the celebration of the Immaculate Conception.
It will be slightly more crowded because you will get people traveling to celebrate the holiday and that includes Italians from other regions.
You may see a slight increase in passengers on the city buses. Just be extra mindful of your valuables.
Shops, restaurants, and many street vendors were open the times I was there. I did not see any closures.
Since it falls on a Wednesday this year, it may affect the amount of travelers - less? Also, possibly many people won't be traveling this year.
There will be a big celebration for the papal ceremony, yes, and the area around the Spanish steps can be very, very crowded. Of course this year dictates changes, so who knows.
Once the ceremony is finished and the police clear the area, about 4 pm, it will go back to its "normal" crowding.
It is also considered by many the kickoff to the official Christmas season.
If they do the Christmas markets in Piazza Navona this year, they probably won't be set up until the 2nd week in December.
On one of my trips to Rome, it did rain for a bit a couple of days - umbrella vendors seem to magically appear at the first drop.
As a norm, many travelers including myself and locals, used an umbrella.
Some women just put the hood up on their puffer coat.
Have fun :)
Edit: ( I will leave the other info since it may help someone else reading)
I just realized that for you, December 8th will primarily be the Transit day.
Termini will still be busy in addition to travelers coming in to celebrate the holiday.
To answer your question about staying in the Spanish steps area, I would choose a hotel closer to Termini.
Each of my trips to Rome, I stayed in the Termini area in the same hotel and never ever had an issue.
Pricing is a lot cheaper. I liked the convenience of being close to the train station. There are plenty of restaurants and shops around.
