Okay, sorry if it's been days, I wanted to give you an update.
I kept a journal of everytime I happened to smell something weird in my bathroom. On October 6 I worked from home, and it became obvious part of the smell came from the vent/exhaust, because I could feel cool air against my palm whenever the neighbour's fan or shower went on. It was quickly followed by a cigarette smell and shampoo smell! However, making my own fan work DIDN'T help suppress the smell.
The morning after, on Oct. 7, I talked to my landlord. We were in the parking at the same time in the morning and I asked him if he would be home at 6 because I now suspected the weird smell was coming from my air vent.
When I came home that evening, he wasn't home yet. It soon started smelling like fresh varnish/paint in my bathroom! I kid you not, the smell was so strong I started feeling nauseated and I had to close the bathroom door and put a towel on the floor, because the smell was starting to spread in the hallway! I called my landlord and asked him if he was on his way, because I had a perfect example of bad smell going on. He was at a hockey game with his son and told me he would be there by 8. Unfortunately, at 8pm the smell had prettu much faded, but my landlord did smell it when he entered the bathroom. He told me all the bathroom exhausts were connected into the same metal ''chimney''. And when he opened the small door we had taped and put his hand in there, it was windy. I mean, it's supposed to work this way I guess, the air goes up and it exists through the roof, but it's not supposed to spread in my bathroom!
He said he would look both air vents/exhausts and put insulating wool (this is a litteral translation, I don't know the right word in English). I also asked him about the ''flapper'' like one of you suggested. He said he didn't know, and that he would check for this as well. He told me he would come back sometime this week, but he still hasn't.
I kept recording every event in a journal because the smells (cigarette, food) happen almost on a daily basis now, and this weekend, I even realized it also came from under our sink. There's a hole in the wall (under the pipes) and it's windy. Although we put a towel to block the hole, it's still an issue.
So for now, the landlord has acknowledged there is a problem with the way the exhaust air is circulating, but the problem is not yet resolved. I've put ducttape over the fan grid in the meantime. The smells still happened over the weekend, but they're less powerful.