Shall is like a stronger form of should

Hello,

There are a few sentences from an exercise on a Russian website for learning English. A subject of the exercise is the modal verb shall. They say shall is like a stronger form of should. I've read that shall is used in this meaning in very formal occasions for example in contracts. But these sentences seem usual to me.

He shall visit his friends more often.
I shall fulfill all the requirements of the contract.
They shall move to our neighborhood.
Why shall I pay for him?
We shan't sign these papers.
Shan't we be afraid to let him down?
Inform them that they shall fill in the forms by tomorrow morning.

What do you think? Would you use them in a conversation?