What does it mean for a menu to be a "set menu"?
Collins dictionary gives a nice definition for a set menu:


  A complete meal in a restaurant or café for a stated price with a limited number of options to choose from for each course [...]


The different serving options are 


family style:
Like you would probably serve food at the family dinner table: every component in its own serving bowl or platter, to be passed round amongst the diners. In a restaurant, often a nice platter of various dishes to be shared.
individually plated:
This is what you are probably expect first when dining in a restaurant - each diner gets his or her choosen dish on his or her own plate. 


So for your case: 
For n diners you build a menu out of n appetizers or starters that get served on one (or a few) platter(s) and is then shared. Of course you can choose n different options or stick to larger quantities of fewer choices.
The main dish comes on n individual plates according to each participant's order and the dessert is again n servings of whatever you pick, like for starters.

And yes, if that is described a set menu, you'll pay a fixed price per person, unless some options are marked with an extra charge, but that would have to be stated clearly on the menu.

You can of course build a menu à la carte instead, then you pick the individual dishes from the à la carte menu - these have individual prices that make up the total cost of the meal.