I had many of these concerns when I took a trip in February.
First, you have to try to calm down (trust me, I know it's hard). But it will really help. When I was at the airport waiting for my flight (REALLY early in the morning) I used the bathroom at the airport and then sat and tried to relax, read a magazine to keep my mind off things.
It is a good idea to get up early to try to get the bathroom trips over with before you leave.
I've never used immodium but many have and say it helps.
As far as sharing a bathroom at the hotel...I know that some hotels have bathrooms at lobby level. You may want to scout them out so you have that bit of information tucked in the back of your mind, that might ease your anxiety about sharing a hotel bathroom.
Buffets...yeah Vegas is full of them but they have regular restaurants too. If you are at a buffet, just choose the best foods you can.
Relax, have fun!