As long as your layover isn't on a Monday (FC is closed then), it's doable more or less along the time frame that you have outlined. You can probably push your return back to PEK T3 to 14:00 if you will already have your boarding passes and your checked bags have previously tagged through to CPH. To your questions:
1) TWOV vs Visa: you'll have to follow whatever status you claimed when you originally checked in at SIN. The airline will enter your status (visa, exempt, TWOV, etc) into the passenger manifest database when you check in, and you'll need to continue to the relevant queue when you arrive at PEK since that will be in Chinese Immigration's database of arrivals. Since you have visas, I'd use the visa queues. While they might be long, there are also more of them. If the single TWOV queue gets buggered up with passengers with issues, you could end up waiting longer.
2) I should think that you will arrive at the FC ticket booths before 10:00. Look for the "Passport" Window and of course, make sure that each person buying a ticket has their passport. And yes, there is security at the FC. You'll go through metal detector and bags will be x-rayed and possibly hand searched. Sizeable carry-ons like rollaboards should be left at the airport Left Luggage counter before you head into town; don't bring them to the FC, but smallish daypacks should be fine.
3) With limited time, you'll have to speed-visit the FC and keep an eye on the clock. You'll probably end up with 2.5 hours inside. Upon exiting the north side, you'll need to walk a bit, as taxis can't hang out anywhere close to the exit location. Plus, they are hard to get on the street in that area. I'd start walking east, and if you have trouble hailing a cab, eventually you'll end up at the Dongsi subway stop where you can get back to Dongzhimen and the Airport Express.