Maria All 3 sentences are fine in English and you will be understood. As a phrasal verb to 'own up' is a slightly less formal kind of expression than to confess, In the second sentence you could say I broke the lamp, but 'it was me who broke the lamp' is perfectly correct informal English (see Michael Swan 'Practical English Usage' section 429. It was I who broke the lamp' is correct but very formal and in practice would be less common in spoken English than the form you have used. 'I failed the exam' (simple past tense) is perfectly OK in spoken English and is particularly common in American English. As Gabriel points out I had failed (or I'd failed) is probably more formally accurate since the past perfect tense is appropriate for actions described prior to other actions in the narrative, e.g 'I owned up to my mother that I had failed....