Does rain interfere with radio reception?

Yes. But it depends on the wavelength and the properties of the rain. In general, one will see interference if the wavelength of the waves coincides with structures in the rain clouds or rain showers. In case of FM radio, the wavelength is on the order of 3 meters. So if the rain shower comes down in sheets which are roughly 3m thick (or multiples thereof), there will be strong interference. Shorter wavelengths like those used by satellite dishes experience scattering on the raindrops themselves. I have seen satellite tv being completely disrupted by heavy rain and snow.

Rain causes change in atmospheric relative humidity, pressure ,temperature and refractive index.

These parameters affect the wave propagation.

Now at heights above 40Km, these effect do not exist. So, radio wave propagation is not affected above this height

There is phenomenon called radio occulation. There is a frequency shift. It involves some maths. check any book on waves.

Generally speaking, Radio reception will be best just after rain is over. Find out why by reading reference book.

Yes it does, rain, fog, high winds, all of these interfere with radio reception.

Yes, but the effect is more noticeable at short wavelengths (high frequencies). That's why many ships carry two radars - a high-frequency one is good for detecting smallish objects, but has difficulty "seeing" through rain; the low-frequency one works better in heavy rain (but may miss small objects).

Yes, the higher the frequency the more prone to interferance.

definate yes even worse when near trees

it's the ice crystals in the clouds that absorb the signal not the rain