In which circumstances are the personal infinitives used? I'm not entirely sure if that is the correct grammatical term, but I am talking about mondanom, mondanod, mondania... etc.? The only construction I know is the one that is used with kell.
The construction with kell (kellett, kellene) is indeed the most common one, but there are some others:
muszáj (colloquial): Holnap muszáj dolgoznom. = I must work tomorrow. szabad: Nem szabad ilyen sok édességet enned. = You're not allowed to / shouldn't eat so many sweets. nincs / nem volt / nem lesz + Q word:
Nincs mit csinálnom. = I have nothing to do.
Nem volt hová mennünk. = We had nowhere to go.
Nem lesz mitől félned. = You'll have nothing to be afraid of. van / volt / lesz + Q word:
Van miért aggódnod? = Do you have anything to worry about?
Nem volt mire büszkének lennie. = He had nothing to be proud of.
Lesz hol aludnod? = Will you have anywhere to sleep?