The title says all. Plus since CX400 lacks a PCI-E connector, I'd require a Molex-to-PCIe connector.
No. No. and No.
HD6870 takes around 220W on load and 1055T has a TDP of 125W. So, if the system goes on full load, there will be just around 50-75W for other components, which would be too less and could kill the PSU on long run (even if it is Corsair). So, get 500W PSU atleast.
Our test system is based on a power hungry Core i7 965 / X58 based. This setup is overclocked to 3.75 GHz. Next to that we have energy saving functions disabled for this motherboard and processor (to ensure consistent benchmark results). On average we are using roughly 50 to 100 Watts more than a standard PC due to higher CPU clock settings, water-cooling, additional cold cathode lights etc.
Keep that in mind. Our normal system power consumption is higher than your average system.
Measured power consumption - 6870
Advertised TDP = 127W
System in IDLE = 172W
System Wattage with GPU in FULL Stress = 291W
Difference (GPU load) = 119 W
Add average IDLE wattage ~ 19W
Subjective obtained GPU power consumption = ~ 138 Watts
Bear in mind that the system Wattage is measured from the wall socket and is for the entire PC. Below, a chart of measured Wattages per card. Overall this is much higher than reference, this is due to an increased GPU voltage to allow easy overclocking and the standard higher clock frequencies.
HD6870 can consume around ~ 138 Watts under load
Now read this ( from guru3d ) :
Here's andtech guys test system specs ( core i7 920 Oced at 3.33 Ghz ) :
and the power consumption result while running a game :
image coutesy of anadtech.com
Source : AnandTech - AMDâ€™s Radeon HD 6870 & 6850: Renewing Competition in the Mid-Range Market
So Cx400W should handle OP's rig safely if he don't OC his CPU or GPU