LiPo battery capacity valid at what discharge current?
Depends on how the manufacturer wants to rate it. Capacity will be reduced at higher current due to internal resistance and chemical effects, but the effect is usually small at rates below 1C (1 hour discharge time). 

Here's an example for a 2C rated battery with a nominal capacity of 660mAh. In this case it appears the rated capacity is expected to be achieved at 1C, with about 5% extra at lower discharge rates.