What are the specific and current code requirements for wiring two circuits to one duplex receptacle?
That's just considered normal wiring

As Ed Beal points out, the only special thing is that since both recpetacles are on the same yoke, they must have a common maintenance shut-off.  Because realistically, repairmen don't actaully stick a tester in both receptacles, they just probe one, and do stuff until it shuts off.  Whatever does that, must shut them both off. 

In the case of the ubiquitous dual NEMA 5 receptacle, you simply have two receptacles on the same yoke, and if you snap off the tabs, they are independent receptacles.  

The grounding system can be blended since it comes out of the same panel, so if you are running two 12/2's instead of 12/2/2 cable, simply tie them together in the back of the box.  You must pigtail them if more than 1 is involved: removing the receptacle can't sever anything else's ground. 

Also if you plan to daisy chain these down to other receptacles, do not put one on the screw and one on the stab.  Either pigtail, or go for receptacles like Leviton's screw-and-clamp which are designed and rated for 2 wires per terminal. 

To your questions


1 Warning signs?  No need, an electrician is expected to measure for power being present, and any of a variety of devices (like a night light) will do this. If you wanted to give them a hint, put "AFCI protected" both above and below the sockets. 
2 Common trip?  Not required.  That would differ from #3 if the installation method was fuses and a shutoff switch. 
3 Common maintenance shutoff?  @EdBeal points out "YES" because they are on a common yoke, based on 210.7 in 2014 and 2017 Codes. 
4 On the same leg, I would call marginally better, but it contradicts #3 so it's not gonna happen.  
5 Risk of 240V arcing? In any case your AFCIs will snuff that right out.  
6 I can't think of anything. 
7 Worrying about the hots touching, you are stuck with it because of #3. 
8 Nothing special about separating receptacles, they are meant to be able to be independent.