The two sentences mean the same thing and that sentence can be written either way. "Turn off" is a Phrasal Verb and, because it takes a direct object ("the radio") it can be split and written as "turn the radio off". However, it is sometimes more clear to keep the phrasal verb together and write just "turn off the radio".

Nothing. No difference in meaning, frequency of usage or in how natural they sound.

These two sentences are the same. All right with the radio. But not all right with the sentence structure. Of course, in spoken language nobody is very accurate... But According to strict grammar rules, the structure of the sentence should be: Future Perfect before Present Simple, so He will have turned off the radio before he leaves the house

There is no difference and they are both used equally. It's a matter of preference.