Learn Finnish: Isä puhui radiossa. - Father spoke on the radio.

Consonant gradation in Finnish only applies to the letters p, t, and k. The basic form of the verb is puhua (to speak). Because there are no p, t, or k sounds in the middle of the word to change, the stem stays exactly the same when we add the past tense -i marker.

Why isn't there a personal ending on puhui for the third person (he/she/it)?

In the present tense, the third-person singular usually doubles the last vowel (like hän puhuu). However, in the past tense, this vowel doubling does not happen. You simply take the stem (puhu-), add the past tense marker (-i), and leave it as is to get puhui.

The English translation says 'on the radio'. Why does Finnish use radiossa (in the radio)?

This is a fixed difference between the two languages. While English speakers talk about hearing something on a broadcast medium, Finns hear things in it. You use the inessive ending -ssa / -ssä (in) for both the radio (radiossa) and the television (televisiossa).