"He can really say anything."
Translation:On opravdu může říkat cokoli.
Because it is optional. We do use it. You do not have to and you might. in some situations you want to use it in some it might be little weird to repeat it if you just used it in previous sentence. Answers without 'on' are also accepted
I'm still quite confused about "říct" vs "říkat". Every time I think I've finally managed to grasp the difference, I still happen to get them wrong.
Is "říkat" the imperfective one?
Yes, "říkat" is imperfective. However, it is possible to use both verbs in this sentence. (Personally, I'd translate this sentence primarily with "říct", but the other is not wrong.)
"Říct" is used for one time, finished actions; říkat for ongoing, repeated, unfinished actions.