It depends a lot on unmentioned details. What's the opportunity cost for you (what are you giving up to go for a one-week trial)? Why would you think it would hurt your chances with other companies? I'd imagine they would pay you. If not, that's a bit of a red flag against the culture.

If the opportunity costs aren't too great, I'd go for it. But I'd make sure it was clear that it was a bi-directional arrangement. I'd be evaluating their culture and my potential co-workers as well to see if that would be a mutually beneficial long term solution. At the end of the week I'd be able to make a more informed decision if the work environment would work out for me.

Not sure how to deal with the compensation on that, maybe 1099 if you are in the US.

I'd look at it (as much of life) as a positive learning experience. Even if you learn nothing technically, every interaction with someone is a chance to see alternate perspectives. In the long run, that's highly valuable.

Pro tip: this should have been posted as a "Ask HN:" not so much "Help me out:". Also I believe this has been asked here before over the years. You might to well to research some of those posts.