This is regarding Future Functions

Hi,
I have been working on 'Future Functions,' and they were a little tricky. I have answered them all, but I need some help to clear some of these up. There is the possibility that I am using will and shall all wrong.

Thanks for the help.

My answer will be written in bold and italic.

Exercise
We have learned in the second module that the modal verbs will and shall are often used before the main verb to indicate a future time.

Look at the following functions and complete the following exercise:

1. A command or order
2. A future possibility
3. An offer
4. A suggestion
5. A definite future event
6. A request

• Shall we go to the cinema? - 4. A suggestion (I know that shall refers to the future, but this to me looks like a suggestion. Am I right to think this? Or always think of 'Shall' as a future possible.)
  
• Shall I carry your bag for you?- 3. An offer (This is a future, but a person has made you an offer to help.)
  
• If it rains, shall we stay at home? - 4. A suggestion ( This sounds to me like: if it rains, instead of keeping to our current plans, should we just not just stay at home)
  
• If you don’t mind, I’ll help you move your stuff. - 3. An Offer ( This has future intent, but this is more like an offer to help; as the person is asking permssion to help)
  
• Shall we go swimming or play squash? - 4. A suggestion ( This to me sounds like a question regarding their day, and they could either spend it by going swimming or playing squash. So, it is a suggestion of how to spend their day.)