It depends on the use of the 10 outlets. 20 amp is the norm. If this is in a shop with heavy loads then you would have to break them up.
If you never plug anything into them, there is no limit. If the total current drawn from all outlets exceeds 20 amps, the breaker will trip.
If the full load amps rating of the motor on the name plate is exactly 15 amps you need to use # 12 wire. If it is a longer run you may have to go up one more wire size. The breaker size you need is 30 amps.
A 30 amp breaker is usually used for a dedicated 30 amp device. Ordinary 15 amp receptacles can not be connected to a breaker of higher trip capacity than the rating of the receptacle. The wire size for a 30 amp breaker is #10 AWG.
No more than ten. If you used a 20-A breaker it would be up to 13.
15 amp will run 8 outlets unless they are going to be heavily loaded. In that case use 20 amps.
If you put a 85 amp breaker in there it will overheat from the starting and stopping of the motor. The extra size of the breaker insures that the furnace will run without interruption and without overheating the breaker. And electric motor can draw three times the amperage rated on start up momentarily. This is why there is need of extra amperage ratings.
If the 12,000 BTU A/C only requires 20 amps to run then yes you can use the same 12 gauge wire but you cannot change it to a 15 amp breaker. You will need to install a 20 amp double pole breaker. If it requires more than 20 amps you will have to replace the wiring and breaker.
#10 cable is no good for 120 amps, you need #2 cable, and it can be used at a distance of 250 ft.
It will work, but the draw backs are that the larger diameter wire is more expensive and it may not fit the 20 A devices well such as the breaker itself and any branch outlets or switches. It is also harder to run because of its bigger size. The voltage drop will be less across the larger wire, so that is likely the biggest advantage if you have a long run.
Yes, you can use lower amperage outlets - the problem would come if you were trying to run a 20 amp appliance on a 15 amp circuit or plug a 20 amp appliance into a 15 amp outlet. It would be better, though, as some kitchen appliances could exceed 15 amps (toaster ovens, some coffee makers, electric griddles, etc.) could try to draw more than the 15 amps your outlets are designed for. Perhaps you could get some 20 amp outlets and use those 15's in a hallway or something less likely to have high amperage draw.
Not legally because the rating of the 30 amp receptacle would have a 50 amp breaker ahead of it. If you reduced the feed breaker to 30 amps and still use the #6 wire, this would be within the electrical code rules.
Anything that does not pull over 50 amps.