What can I substitute "shall" with in these sentences to sound less formal?
You look cold. Shall I put the heater on?
What shall I bring you, tea or coffee?
Just to add further, and more informal alternatives to Walter’s answer.
You could say to a friend:
You look cold. Do you fancy the heating on? (very informal)
You look cold. Do you want the heating on? (informal)
You look cold. Would you like the heating on? (less formal)
Fancy a cup of tea? (very informal)
What / How about a nice cup of tea or coffee? (informal)
Would you like tea or coffee? (less formal)
Source : Link , Question Author : Graduate , Answer Author : Mari-Lou A