Can i discharge/charge/store(cycle) two 5800 mah lipos at same time at 12 amps(one batt. Per channel).

First of all: there's a thread on the 406 Duo.
The 406 Duo can even charge two 6S Lipos at 40A each at the same time, so 12A is no problem (capacity is not a factor in this) - question is, if your power supply has enough juice for either...
Discharge is limited to 10A per channel without external resistors, IIRC.
Storage just uses charge or discharge settings as above, and stops at the set storage voltage, so no different limits apply.

Discharge is limited to 80w per channel (or 140W total) without setting up another discharge mode. So yes, this is roughly 10A for 2s, higher for 1s, lower for more cells.

As was mentioned before, it's most likely limited by the power supply (voltage and current). For example, I run my 406duo off a 12v/63amp power supply. The 406duo is limited to 60A input, so I can only get about 720 watts of charging power. Half of it's rated 1400 watts. To get full potential I'd need a 24v power supply. But I don't need it.

Quick math is: # cells * 4.2v (assuming regular lipo not HV) * charge amp rate = charge power in watts. If you're doing 2 batteries at same time, multiply that number by 2. That's the min wattage needed. But not all power supplies are created equal. Some have pretty bad voltage sag as you get close to their rated capacity.