I'm asking from my friend this because we had already planned a visit to the beach no full stop here So, and I want to just confirm the plan. I want to make sure that he hasn't cancelled the plan changed his mind. It's not a suggestion. I think "shall" is for suggestions. purpose.
Note my changes above. If he had cancelled the plan, you would already know that. Cancelling it would have involved telling you. You're checking that he still wants to go.
As a side note, my comment about English in Ireland refers to suggestions but it's also used to mean "Do you want ...?"
Irish English: Will we go to the beach?
British English: Shall we go to the beach?
Irish English: Will you have a cup of tea?
British English: Do you want a cup of tea?