Not a long ago, I saw a friend of mine ask his collegue: "When you will stop to work?" (Meaning "at what time are you going to finish your work").
His collegue then asked him back:"When will I stop to work?" or "When will I stop working?"
My friend told him that both are the same, and then his collegue said: "No, they aren't the same". but didn't give any explanation for that. I'd love to confirm the difference bwteen these two and get the explanation.
There are not general rules for this sort of question: it depends on the requirements of the particular words.
Stop takes a noun phrase or an -ing clause: it doesn't take a to infinitive clause. I don't know of any reason for this: it just happens to be how current English is.
Cease has a similar meaning to stop, but it can sometimes take a to infinitive clause as well as an -ing clause. (Though there is a subtle difference of meaning: cease to work would talk about a the end of a habitual activity, whereas ceased working could be either habitual or referring to a particular activity).
So When will you stop to work? is not grammatical in any current English as far as I know.
[Note on a possible confusion: you do sometimes meet "stop to infinitive" but it has a different meaning. "When I stop to think" = "When I stop [in order] to think", not "When I stop thinking".]
When will you stop to work? is indeed an unnatural phrase.
I might ask this of a robot, or there might be a context in which stop can be understood refer to fooling around, which needs to stop in order that some work be done!
Note that this last interpretation is pretty much the opposite of what the question poser meant to convey.
In general, non-native speakers tend to overuse to+infinitive constructions where e.g. -ing forms are more appropriate.
