Weird questions about menstrual cups

Hi everyone, I'm trying to decide if I should switch to a cup or not, and there's two things holding me back. If anyone has an answer it would help me immensely :)

1 - basically when I use a tampon i need to change it when I go poop. This is because of how I seat and the type of strength I make, usually the tampon comes out halfway so I end up having to change it. Will the same happen with the cup?

2 - I use about 3-4 super plus tampons a day, maximum 5. Is this flow for more than one cup? Will I have to change through the day?

The reason I can't change is that my works toilets don't have the wash basins inside the stalls, so it would be very hard to wash and replace without making a mess in front of other people.

Any help appreciated xoxo