Is it rude to decline food at dinner parties?
No, there could be many reasons why you would (dietary restrictions, food allergies, etc.)
No, as long as you eat something.
Only if it's buffet style (i.e. everyone's called to help themselves)
Should hosts try making sure there's something for everyone?
No - you're not a restaurant
Depends on the number of guests
Yes, it's common courtesy
That's why they invented potluck dinners