I am an independent researcher and have recently been solicited from the director of a university research lab to see what potential there is for collaboration. They found some of my papers and thought they were of sufficient interest to reach out. I just received an email from the director stating that my papers are being read by their team and the purpose of the email is to start a discussion about collaborative opportunities. Having never conducted research in academia, I don't know what I may be walking into. I don't know the culture and what the upspoken expectations are. What kinds of questions might I ask? Is it acceptable to seek funding from them? I am hoping someone can provide feedback on these limited facts.
Usually this is a rare constellation. Normally, independent researchers seek ways to publish and/or to connect with academia.
Basically, you need to consider authorship, IP, and funding (if applicable).
Authorship: the main currency of academia is authorship. If your contribution is the most important part of this work, in your negotiation you should find out how they intend work with you and how to publish the work. You could then ask about authorship.
IP: will there be any IP that is going beyond publication interests? Something that might become a patent or make money? Are you interested in that? If so, you probably need to be a bit more careful. NDAs might be relevant, but this also begins to move into legal territory, so off-limits to SE. If you do not see any commercial interest however, this is nothing to worry about (of course, you might find yourself unlucky that you let some highly profitable idea fly - but then, by far most ideas do not make money)
Funding: you have to distinguish if you wish payment as a contractor or as a (possibly temporary) university employee and covering expenses of the research (computers, travels, etc.). You have to find out if and in which form such money is available, if at all, and if it is not if you want to continue. If the project is very interesting, you may consider collaborating with the university in getting funding. Note that some institutions' bureaucracies heartily dislike working with individuals which means that you might have to set up a company for that purpose.
Finally: If you do not care about being paid, then you can ignore 3. Talk to people, find out whether you like what you hear, and have fun doing some research.
I suggest that you have a conversation with them, preferably face to face or, if that isn't feasible, using something like Zoom. Ask about how they envision a collaboration and what each might be willing and able to contribute. You might be able to arrange to have them fund a visit to their university if you are remote. That would be a good start and provide the opportunity for the discussions. It would also indicate good faith in their offer/interest.
If it is about a specific project of yours then talk a bit about authorship, probably making it clear that you are the principal. If it is more general, about an area of mutual interest then talk about the dimensions of that.
Only then should you talk about funding and it might not be them funding you, but mutually seeking funding from elsewhere.
Such things can have a future and be mutually beneficial. It is also possible, though less likely, that you wind up being exploited. Collaborations need to have active participants and a sharing of ideas.
I think it is worth exploring (usually), but don't make decisions until you know more and are comfortable.