Learn Italian: Pensavo di schiarire un po' i capelli. - I was thinking of lightening my hair a bit.

This is the imperfetto attenuativo (mitigating imperfect). Even though you are talking about a present intention ("I am thinking of..."), using the imperfect tense softens the statement. It makes you sound less demanding and more open to suggestion, which is very common when talking to a hairdresser or retail worker.

Why is the preposition di used between pensavo and schiarire?

When the verb pensare means "to plan to" or "to think about doing" an action, it must be followed by di plus an infinitive verb. So, pensare di schiarire translates to "to think of lightening".

The English translation says "my hair", but the Italian just says i capelli. Why isn't there a possessive like i miei?

In Italian, you generally drop the possessive adjective (like miei) when talking about body parts, clothing, or hair, as long as it's obvious who the owner is. Since you are the one doing the thinking (pensavo), it's automatically understood that you mean your own hair.

Why does un po' have an apostrophe at the end? Is that an accent mark?

It is an apostrophe, not an accent mark. Po' is short for poco (a little). The apostrophe indicates that the final syllable (-co) has been chopped off.