There only two currently published questions in Sindarin (and none in its conceptual precursors): linnathol? “will you sing?” from 1969 (PE22/167) and man agorech? from the early 1950s (VT50/5), untranslated but almost certainly meaning “what have we done?” using the late-1940s, early-1950s 1st pl. inclusive pronominal suffix -ch (VT50/21-22). These two questions give us a fair amount of information, though. The first demonstrates that a question can be indicated by intonation alone, without any special question words. This second indicates that a question word at the beginning of the phrase like man “what” can be used to indicate a question. This is consistent with Quenya question formation.
There are, unfortunately, almost no attested question words in Sindarin; the aforementioned man “what, (?) who” is the only one. Fiona Jallings suggested a more comprehensive set of interrogative pronouns in her book A Fan’s Guide to Neo-Sindarin based on the contraction of various prepositions with man (FGNS/220-221). I recommended adopting her approach, though in my own list of interrogative pronouns I suggest *mallú for “when” rather than her *neman (mostly because I don’t think ne means “during”).
When responding to questions, you have several options. We don’t know the Sindarin word for “yes”, but many Neo-Sindarin writers now assume it would be *naw, the equivalent of Q. ná “yes, it is so” (PE22/166). For “no” you can use û (PE17/144), or if you prefer la-negation you can use the neologism *law. In response to a request you can say either athon “I will” (PE22/167) or avon “I won’t” (PE17/143; WJ/371). When answering for a group: athof “we will” or avof “we won’t”.