Learn Turkish: Bardak dolunca musluğu kapat. - Turn off the tap when the glass fills up.

Both mean "when the glass fills", but -unca often carries the nuance of "as soon as" or "right upon" an action completing. It links the two events closely in time: the moment it becomes full, turn off the tap.

Could I use a -laş verb here instead of dolmak to mean "become full"?

Not naturally. While the -laş / -leş suffix is perfect for turning adjectives into "becoming" verbs (like güzelleşmek for "to become beautiful"), "full" (dolu) is a bit of an exception. Instead of forming dolulaşmak, Turkish just uses the root verb dolmak (to become full, to fill up).

Why isn't there an accusative marker on bardak?

In English, the verb "fill" can be transitive ("I fill the glass") or intransitive ("The glass fills"). In Turkish, dolmak is strictly intransitive ("to become full"). Since the glass is doing the action of becoming full, bardak is the subject of the -unca clause, not a direct object, so it stays in its bare dictionary form. If you wanted to say "when you fill the glass", you would need the causative verb doldurmak and the accusative case: bardağı doldurunca.

Why use kapat instead of kapa here?