"Ich bin da schon besser integriert als er."
Yes, or even just present tense with an adjective. I think "integriert" can be also regarded as an adjective.
I definitely read it as present tense with an adjective. I can't remember what the form for the verb in called. There are actually German verbs were the forms are different for this and for passive voice, iirc.
I wrote "I am better integrated there yet than he is". duolingo tells me the "yet" is wrong, I took it because of the "schon" in the German sentence. Since I am a native German speaker practicing english, can anyone tell me if and why the "yet" is wrong?
"Yet" is usually used in negations, like "I have not done it yet". In affirmative sentences it would rather be "already". I am already better integrated there than he is. However, this word is not as widely used in English as "schon" is in German, so quite often "schon" is left without any particular translation.
I'm not a native English speaker either, just sharing my thoughts.