could this also be 'one exercises every day'? If not, how would you say that?
That would be "ci si esercita ogni giorno"; ci in this case is an impersonal verbal predicate, needed only because there would be no way to distinguish the impersonal pronoun si from the same reflexive pronoun (esercitare / esercitarsi). When a reflexive verb exists, si usually assumes that meaning.
Edit: Note that if an object were provided, the reflexive verb would be ruled out and the sentence would become impersonal, e.g. "Questa professione si esercita ogni giorno" (one practices this profession every day).
I'm not sure, but I think that you have to use the verb "fare". Lei fa gli esercizi ogni giorno.