Arriving by Air China (domestic) in PEK T3 around 11.20 and leaving with American Airlines at 16.20.

Yes, you totally have enough time to make this connection.
You don't need to take the inside train because both your airlines are in T3. And the correct procedures are the following:
1:Flight Arrival & Transfer Procedures
2:Inspection & Quarantine
3:Exit and Entry Frontier Inspection
4:Security Check
5:Customs inspection
6:Waiting & Boarding
Baggage Claim is not the necessary step. Don't worry.