Can I use 'ask' and 'ask for' interchangeably? For example, there's no difference whatsoever (including stylistic difference) between 'ask forgiveness' and 'ask for forgiveness', is there?
Generally, you can't. For example, if you replace the phrase 'ask a question' with 'ask for a question', it will turn question into requested thing: the preposition 'for' here precedes that thing (= the person who asks would like to be asked a question). Sometimes, in informal speech that preposition (before the desired 'forgiveness' in your example) is omitted, but it can't be added into a phrase about asking a question.