Learn Dutch: Ik was de kwast zelf, want we hebben net geklust. - I am washing the brush myself, because we just did some odd jobs.

In this sentence, zelf highlights that you are doing the action personally ("myself"), rather than having someone else do it. If you used alleen, it would mean you are washing the brush "alone" (without anyone else in the room). Since the second half of the sentence says "we just did some odd jobs", you probably aren't alone, but you are the one doing the washing!

Doesn't was mean "was"? Why is it translated as "am washing"?

Was is indeed the singular past tense of zijn (to be). However, here it is the first-person present tense of the verb wassen (to wash). You can figure this out from context: "I was the paintbrush" doesn't make much sense, but "I wash the paintbrush" fits perfectly.

Why doesn't want push the verbs to the end of the sentence?

Want (because) is a coordinating conjunction, just like en (and) or maar (but). It connects two normal main clauses without changing the word order. If you had used the word omdat (which also means "because"), it would push the verbs to the end: ...omdat we net geklust hebben.

What kind of verb is geklust?