Higher volatility means more premium in the options. This means there is more theta in the option, or more decay.
Sure. Let's say there are 100 days remaining until expiration. Compare two scenarios - one where the ATM xyz 100 calls are worth 3 (higher implied volatility), and the other where those same calls are worth 2 (lower implied volatility). In both cases, we know that in 100 days that call will have time premium of zero. In the first case (higher implied vol), time premium goes from 3 to 0 in 100 days. In the second case (lower iv), time premium goes from 2 to 0 in 100 days. Obviously, in the first case daily time decay is greater than in the second.
I look at it in this way: You are choosing between gamma and theta to profit from the market. Higher volty means an increase in the probability of market movement (gamma), which must be offset by higher premiums (theta) to compensate the option writers.
Or, you can look at it this way, time value affects the extrinsic value of an option. Implied volatility increases the extrinsic value. It has no affect on intrinsic value. The more extrinsic value, the more value that can be lost due to time decay.