A network analyzer is ideal to test your first two circuits. The network analyzer applies a swept-frequency RF stimulus to one port of your circuit and measures the response at the same or a different port. A scalar network analyzer only measures the response magnitude and a vector network analyzer measures both magnitude and phase.
The key to obtaining accurate measurements from a network analyzer is calibration. Essentially this means testing known standard devices to determine the performance of the network analyzer, then using this knowledge to correct the measurements you do later on your device under test (DUT). More and more complex types of network analyzer allow testing more standard devices to obtain more and more accurate final measurements. Your network analyzer will come with detailed instructions on how to do the different calibrations that it supports.
So for a butterworth filter, you calibrate your network analyzer, then connect your DUT, measure the response, and check whether it matches the ideal response of a butterworth filter. If you also have specs on return loss, you could check those at the same time.
For a power amplifier, you would measure the response and see if the gain is what is required.
If you want to test your PA for harmonic distortion you will rather have a synthesizer and a spectrum analyzer. You apply an input at different frequencies and power levels using the synthesizer, and use the spectrum analyzer to measure the power in the output fundamental and harmonics.
For an RF detector, you would apply a stimulus using a synthesizer and measure the output using a multimeter.
For the comparator, you will probably need to set up something more complex -- your set up will probably involve an osilloscope. What you test will depend on what are your critical specs and how your final system will work.
