A mirror only needs one precision surface. A lense has 2. Lenses are formed by pouring molten glass into a mold and then polishing. It is very easy to get air bubbles trapped in the glass during this process. Mirrors have a reflective coating that can fill in any small inperfections and create a smooth surface.
Radio astronomers can make observations day or night, as long as the object is above the horizon.
The Sun puts out very little radio light, so there is no background signal to hide the very small radio signal from space, like there is with visible light. Radio waves have very long wavelengths and travel through clouds easily. X-ray and gamma ray wavelengths are not able to travel through Earth's atmosphere. In other words, the atmosphere is opaque to those wavelengths. Therefore, any study of x-ray and gamma ray light from space must be done above the Earth's atmosphere.