Learn Hardcore Latin: Mater aquam puram bibit.

Because mater is in the nominative case, which is the normal case for the subject. So mater = the mother (the doer of the action).

Why is aquam spelled with -am instead of aqua?

Because aquam is accusative singular, used here for the direct object (the thing being drunk).

aqua = nominative (water, as a subject)
aquam = accusative (water, as an object)

What does puram do, and why is it puram (not purus/pura/purum)?

puram is an adjective meaning pure/clean, and it describes aquam. Adjectives agree with the noun they modify in case, number, and gender:

aquam = feminine, singular, accusative
therefore the adjective is puram = feminine, singular, accusative

Is Latin word order fixed? Why isn’t it Mater bibit aquam puram?