For a first order system, what type of response to a sine wave?
A first order system will produce an output which is also a sine, but with a different amplitude and phase. Because the differential of a sine is also a (phase shifted) sine of the same period, and the output of a first order system is a sum of the input and the differential of the input, there is no other possibility - you are adding two sines with the same period and that can only result in amplitude and phase change, not a non-sinusoid.

Once you start considering slew rates and other limits, you no longer have a linear first order system, so it may be distorted. Given a slew rate, and the first order equation, you can determine the frequency that linearity breaks down from the maximal gradient of a signal of given amplitude.