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In the circled part, what is the harmony?

Is the E-flat a non-chord tone or is this just some weird chord? (I've only learnt basic harmony.)

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I would view that E♭ as a non-chord tone above a V7 (D♭) chord.

More specifically, I would view this as a passing tone between the F in m. 3 and the D♭ in m. 4. This means that the entirety of mm. 3–4 is best understood as a V7 chord. The E♭ on beat 2 of m. 3 is just a passing tone from the F right before it, and Chopin repeats this passing-tone E♭ on the second eighth note of m. 4 before resolving it to the chord-tone D♭.

And if you're really interested, this E♭–D♭ motion is actually a little conceptual motive throughout the entire piece. (As a couple little examples: look at the first three chords and the cadence right before the coda!) Perhaps Chopin did this intentionally, perhaps it was a byproduct of this being a heavily pentatonic piece (hence the nickname "Black Keys," which themselves create a pentatonic collection), perhaps it's just a part of nineteenth-century compositional practice, or perhaps it's a little bit of all three.

In any event, be prepared to find more of these little E♭–D♭ patterns in this piece!

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