Learn Portuguese (Portugal): Quando termina o jantar?

In Portuguese questions that start with a question word like quando (when), it is very common and natural to put the verb before the subject. So, instead of saying "When the dinner finishes", you say "When finishes the dinner" (Quando termina o jantar?).

Where is the word for "does" in this sentence?

Portuguese doesn't use helper words like "do" or "does" to make questions. The single verb termina (finishes) handles the action all by itself. So, Quando termina... translates fully to "When does... finish?".

What is the infinitive (dictionary form) of termina, and is it regular?

The verb is terminar (to finish / to end). It is a completely regular -ar verb. Here, it is in the "he/she/it" form because it refers to a singular thing, o jantar (the dinner).

Since this lesson also teaches a que horas, could I say A que horas termina o jantar? instead?

Yes, but it changes the meaning slightly! Quando simply means "when", so the answer could be a general time like "soon" or "in an hour". A que horas means "at what time", which specifically asks for an exact time on the clock, like "at 10:00 PM".