I made it write poetry and sometimes, the output doesn't seem to be grammatical or correct at all. Is it ok if I base some of my questions on output generated by ChatGPT?
I can't think of a way this could be a good idea for the site.
Since you're a high-rep user with many successful questions, I'm sure you know that all questions on this site must be about learning some specific aspect of the English language. Proofreading questions are off-topic, so you would have to frame your question about some aspect of ChatGPT's language use, like a grammar point or vocabulary use that you are unsure about. This is probably not an issue with you, but worth mentioning up top because I'm sure many learners here have similar ideas.
The only situation where we are lenient about the proofreading rule is where the cited passage is from a highly reputable source, like a prominent news organization or a respected dictionary. These sources nearly always have very high-quality, natural English, so if a learner believes it's wrong, it's usually an opportunity for learning, so a great question to ask. And I love answering those questions. But ChatGPT is not at all such a source.
Further, if you're asking it to write poetry, this gives it licence to ignore the rules of grammar and vocabulary usage, so that might be what you're encountering.
And FWIW, the reality on this site is that a good portion of the users here strongly dislike ChatGPT, and will DV/CV on sight and take to the comment section or even Meta to rally support against it.