'Supposed to be' can be used to mean 'it is said/believed'.
- The new James Bond movie is supposed to be excellent.
- He is supposed to have been rude to Mark but I don't believe it.
- It is supposed to be the best restaurant in town.
'Supposed to be' can also be used to talk about what is arranged, intended or expected. It is a bit like 'should'.
- I'm supposed to get to work by 8.
- John is supposed to turn off all the lights when he leaves.
- I'm supposed to pay my rent on the first of the month.
- It's not supposed to be here.
Often there is a suggestion that the action 'supposed to' happen does not actually happen.
- I'm supposed to be there before 8 but I'm often late.
- You were supposed to phone me.
- I'm supposed to be getting on a plane to Tokyo at this very minute.
'Not supposed to' often suggests that something is not allowed or prohibited.
- You're not supposed to smoke in here.
- I'm not supposed to tell you.
- We're not supposed to use the Internet for personal reasons at work.
'Suppose' can also be used as a conjunction to mean 'what if'. Notice that the verb which follows it is sometimes, but not always, put 'more in the past'.
- Suppose we take the earlier train to Munich? It would give us more time there.
- Suppose we took the plane instead? That would give us even more time.
- There's nobody in reception to let our visitors in. Suppose I sit there until somebody comes?
- I'm going to ask him for a pay increase. ~ Suppose he said 'no'? What would you do?