CA is the best carrier on SHA-PEK route. Same on PVG-PEK route. It's their signature domestic route, aka the one they have to be good at to impress travellers. CA gives you the advantage of landing in PEK Terminal 3, where your JL flight would depart. You might not want to try a inter-terminal transfer at PEK, especially if you are pressed for time.
Double check the operating carrier, as they c/s every flight on that route.

Domestic to International baggage interline is very unlikely. It might be possible if your departing airport is PVG rather than SHA, but its a long long shot either way.

JL check-in counters close 1hr prior to scheduled departure, regardless of the class of travel.

If landing in T1 or T2 - 1.5hr to be on the safe side.
If you land in T3, - 45 minutes.

Both assuming, of course, that you won't get lost or experience delay in claiming your checked baggage.
ps. Don't worry about getting lost if you're in T3, just approach one of the many airport guides circulating throughout the terminal to help you find your way. (the skiny and tall Chinese ladies in traditional costume)

If you have lounge access, checking in at 1hr before departure will give you only about 5 minutes of lounge time.

This is where the fun begins . At PEK they periodically add on numbers of check stations you must go through on departure.

A flow chart of what happens after check-in:
Boarding pass check (1 min) > Train Ride (5 min) > Quarantine Body Temp Scan (walk through) > Immigration Passport Check (5~35 min, make sure you have your departure card filled in) > Customs Check (5~15 min) > Security Check (5~20 min) > Walk to gate (5~ 15 min)