Learn Hardcore Finnish: Otan kirjan repusta, kun odotan bussia pysäkillä. - I take a book out of the backpack when I wait for the bus at the stop.

Finnish usually drops subject pronouns because the verb ending shows the person. otan already means I take (root ota- + -n = 1st person singular). You can add minä for emphasis or contrast, but it’s not required.

What tense is otan and odotan? Could it also mean future?

Both otan and odotan are in the present tense. Finnish often uses the present to talk about near-future actions too, so depending on context the sentence can describe:

something happening right now / habitually, or
something you’re about to do (no separate future tense is needed).

Why is kirja in the form kirjan?

kirjan is the object form used for a total/complete object here: you’re taking the whole book (one complete action). In traditional terms, this looks like the genitive in the singular (kirjan), but functionally it’s the common total object marking in present-tense affirmative sentences.

Could it be otan kirjaa instead of otan kirjan?