Learn Italian: L'esaminatore mi ha bocciato perché ci ho messo troppo tempo. - The examiner failed me because I took too much time.

The verb here is metterci, which we use to express how much time a specific person takes to do something. In the passato prossimo, metterci always takes the auxiliary verb avere (like ho, hai, ha). You would only use essere if you were using the other time verb, volerci, to say how much time is needed in general (for example: ci è voluto troppo tempo).

Would messo ever change its ending here, for example if a woman was speaking?

No. Because metterci uses the auxiliary verb avere, its past participle (messo) is invariable. It stays exactly the same regardless of who is speaking or how much time was taken. This is a key difference from volerci, which uses essere and requires the participle to agree with the time.

Does the ci in ci ho messo mean "us" or "there"?

Neither! Here, ci is simply a built-in part of the phrasal verb metterci (to take time). You must include it for the verb to make sense, but it doesn't translate to a separate word like "us" or "there" in English.

Could I say ho bocciato l'esame to mean "I failed the exam"?