When an academic is invited to give a talk at another university, are their food and travel expenses usually fully reimbursed by the university that invited the professor?
The short answer is that it depends (no surprise there). If it's to give a talk in a department colloquium or seminar, travel cost are usually covered (at least, that's been my experience in mathematics), though that can vary a bit, especially since smaller departments may have very limited budgets for that kind of thing.
Food expenses vary even more wildly, and they depend heavily on the source of funding. I've been at places that had a standard per diem for visitors, places that did nothing, and places where the faculty would take the speaker to dinner and split the cost among them.