I have flight to SFO to beijing (1 hour) stop over then connecting to mnl. Is 1hr enough to catch

We have flight Air China from sfo-PEK (1hour stop over/terminal 1) then connecting to Manila flight (terminal 3).
Questions:
A.) Do we have enough time to catch our flights in 1hr.? I have children with me.
B.)is there anyone can help or assist us to speed our line when we go to immigration or security check?I worried that we might miss the flight?
3.) If we miss the flight , I don't think it's our fault if we didn't make it due to the time constraints the airline gave us?
Asking to help or any advice to ease the worries. Thanks.