Yes, plenty of award tickets within China for both airlines using United's miles. You're too early though. Awards are bookable 330 days out, and the airlines do not necessarily release them this far out.

As for revenue tickets - the sweet spot to book is anywhere between T-3 months and T-1 week. Things may change for next year, but I wouldn't book revenue tickets more than 3 months out. I would also advise not using any international sites to book domestic tickets - you'd be overpaying. Ctrip (if you can get through the Chinese interface) or Trip.com (same company) or Qunar can help you book. Air China and Shenzhen airlines both have decent English websites. Just make sure you choose China as your location to get best prices.

Two caveats to note
1. If there are IRROPS you may end up banging your head against the wall to get the tickets reissued with new flight numbers. I needed a Chinese speaker to help me with this. The phone agents didn't want to touch the ticket (needed to escalate), and there was no airline ground staff at the outstation, only contracted handlers who could do nothing with the ticket.
2. If you book an award ticket, your passport/document number will not be in the system (as is common for all intra-China flights) and you'll get questions asked at security as to why you don't have it in the system (I've never been stopped from flying though).