So Vil i gerne have is formal and Vil du have is informal?
Adding "gerne" does not make it formal, it makes it more polite, more request than demand.
"Vil du have"- do you want.
"Vil du gerne have"- would you like to have.
Will you have an apple? Do you want an apple? What would be the difference? Just looking for input.
In the case where you are offering an apple, both have the same meaning. However, being pedantic, the first asks 'Will you be in possession of an apple?', and the second 'Is having an apple something that you want?'
what about would you have versus will you have...it appears sometimes would is accepted and sometimes will is accepted...