"I am drinking his beer."
Translation:Mi trinkas lian bieron.
Drinki has two meanings.
Drinking alcoholic beverages
When drinki comes in that sense it DOES NOT have a direct object (intransitive verb).
Drinking excessively with intention of having fun
When it comes in that sense, it may have a direct object (transitive verb).
This is covered later in the course. "Mi estas trinkanta" is the present progressive tense of the verb. It means "I am drinking" as opposed to "Mi trinkas" which is in the simple present -"I drink". In general conversation, we usually use the simple present tense, unless we really want to emphasise that the action is happening right now, at this very moment. English tends to use the present progressive a lot more than Esperanto.
No. We put an -n on the ends of words when they are the object of the sentence. "Lian bieron" is the object of "trinkas", so the -n is required. You can read more about this in the Tips & Notes for Accusatives: