It means you do not have to pay for dinner,either it is free or someone else will pay for you. This idiom usually means the 'house' or restaurant owner will pay for not 'anyone'.
She probably likes you and wants to get to know you better.
it means: "that person is casual".
he wants you
It is a mix between the casual and sophisticated look...
casual
formal means to be casual and not so important just for taste
"Dinner on the house" means that the meal is provided free of charge. It is often a gesture of goodwill or appreciation from the establishment, such as a restaurant, towards a customer. It can also be given as a form of compensation for a mistake or inconvenience.
Dressing casual means slacks and a dress shirt and nicer shoes.
it means dinner or the dinner
If you mean professional cook, then plenty of experience and possibly a culinary degree thrown in. Bear in mind anybody can consider themselves a "cook," even if it's just a parent making dinner for their family.
casual observation