How long will ranked be down for after the season ends?

Tomorrow’s the last day, I think? So preseason will last from then to early January? Your rank won’t reset until the new season starts, and whatever ranking you do in preseason will still count towards your placements.

Ranked won't actually be down. Your MMR base rate can still change, and you can still play ranked. However, it's ONLY to play and either tank or raise your base for a starting average for the next season. There's no reward or permanent rank for doing it.

Suppose you end the Season Silver II. You can still grind to Gold I over the Preseason, and when Season 10 placements start, it will use the Gold II averaged with a baseline (1550 MMR) to distinguish your placement matches. (Gold I averaged with 1550 is about Gold III).

If you on the other hand stay at Silver II, your baseline start will be about Silver I.

This is EXTREMELY important, because it impacts your fresh season ability to climb. If you stay Silver II-I, the result is you've burnt all your MMR adjustment by the time you just get to Gold IV. If You start at Gold III, you might be up to Gold I/Plat IV by the time you average down to ~ 18 LP a win/18 a loss.

Then again.... you could end a season at Silver II, and demote down to Bronze I too.... and be forced to start even lower.