"Which František are you waiting for?"
Translation:Na kterého Františka čekáte?
Not really connected to that specific example, but it made me think about it: Czechs sometimes use "plural you" to refer to "singular you" to be polite, right? How close do you need to be use singular you?
Hard to say. It's more of a question of customs and manners, and even natives have sometimes problems to discern when it is appropriate and when not.
A few pieces of general advice that I could give you, stick with 'vy' at first, don't address someone using 'ty' unless you shake your hands and there's some kind of an introduction. Then it depends on the situation, your/the other's social status, position of authority, age, gender etc.
To illustrate it a bit: using 'ty' with newly-made friends of your age in a pub/café is perfectly appropriate, the same for your new roommate, classmate etc. Using 'ty' to address the mother of your SO/your new boss at work after you've just been introduced to her would be seen as rude. The same with using 'ty' to address your much older female co-worker, unless she has given you leave to do so. You wouldn't use 'ty' to address your customers or clients as well.
When in doubt, ask or offer using 'ty'. But you should know that the person with the 'higher status' offers first.
To confuse matters further, we sometimes use first names with plural 'vy' forms. That's kinda semi-formal. Your boss might address you like that. Or your teachers.
What would happen if you address someone who shouldn't be, informal? Just curious? How bad is it?
Pretty bad sometimes, one notices immediately and the reactions can be of various kinds depending on the situation, the age difference, the social class and so on. Sometimes it creates very awkward situations when you do not know which one to use.
What would the word order be for a verb that uses "se", such as "Which František are you interested in?"
"Na jakého Františka čekáš?" ....... přijde mně to významově úplně stejné
Tak to vám připadá špatně. Přiznávám, že do jisté míry se v hovorové češtině rozdíl mezi "jaký" a "který" stírá, nicméně stále existuje.