There is a slight difference between " offers" , 'requests' and advice.
In this case , it's suitable to use shall with the pronoun " I " better than
will .Do you agree on this? With best wishes.
In this situation we better use shall - Shall I help you ?[I offer my help]
I will do that - willingness-
I shall do that - obligation; duty
Mother : Will you help me with the dishes?
I ; Yes, I will .[ I do it with pleasure]
: Yes, I shall [no pleasure, I`ll do it because mother asks me]
Shall I help you ?- - I offer my help
Could I help you? - more polite
Would I help you? - polite