1. You either say:
a) 'I am going to pay the bill.' - The 'bill' is a receipt that states all of the items you have ordered, their individual costs, and their total cost. 'I am going to pay the bill,' means you are going to pay the total cost of all the items you have ordered. You cannot say 'I am going to pay for the bill,' because the bill is not an item you have bought.
Or:
b) 'I am going to pay for my order.' - The 'order' refers to all of the items you have ordered. 'I am going to pay for my order,' means you are going to pay for all the items you have ordered.
2. 'I'll foot the bill' makes sense, but you will hear more often 'I'll pay' or 'I'll get the bill.' 'To foot the bill' is seen more often in written English than in spoken English.
3. It depends on what you want your meaning to be:
a) 'I have dinner with someone else.' - I have dinner with someone who is not you.
b) 'I have dinner with others.' - I have dinner with multiple people.
I hope this helps you!