Should I accept review requests from dubious journals?
You have no obligation to accept reviews from any journals.
In the long term, you should of course accept review tasks, since the review system is built on everyone doing their part in return for the reviews you get on your own papers. But if you think the journal is not serious, there is no need to waste your time on a review.
The problem will lie in identifying what is real and what is not. Apart from researching the journal yourself, as you have done, you should also ask more senior scientists of their opinion.
Edit: Following up on the request for additional input on whether reviewing for dubious journals could be harmful in some way:
I think the greatest risk is that you may provide legitimacy to a journal that is not legitimate. It may be harmful to you if the journal in some way represents, let's say, creationism, in that you may become associated with something you really do not support.
I do not see any clear problem for the authors whose paper you review. Their greatest problem, assuming they are common scientists, should be that they submitted it there in the first place.
Personally, I delete all e-mails with requests from journals I do not know of. I know the journals in my field, and the new serious journals that have sprung up have a firm basis in the community, so they are also "known". I do check on some of these unknown journals occasionally, out of curiosity, and I particularly check the sort of papers they publish and the editors of the journal. That usually tells me if the journal is of interest.
Some of these journals may be legitimate, but they end up being extremely narrow regionally in terms of the origin of their authors and editors, and thus probably also their readership. A new journal is a difficult thing to get accepted unless you start with a wide base in the community, so some of these journals may be very legitimate but still have to prove themselves somehow. The problem is how to distinguish good from bad, and that is truly not easy in many cases.
I might actually be doing more harm than good (to myself, to the authors, and/or to scientific publishing in general) by agreeing to review a manuscript sent to me by a sufficiently scammy journal.
Yes, exactly. Don't encourage predatory publishing. Don't encourage the authors, who almost certainly have no interest in your feedback and just want an additional publication, hoping it will help them get that cosy government job/tenure in a university that doesn't care about quality. All of this is a simulacrum of science.
if nobody agreed to review manuscripts for them, how could they ever improve their review process
True, but you shouldn't worry about it. Because we don't need more journals, especially not pay-for-publish, low-quality journals.
You probably know very well which are the good journals in your field, and if you publish (or even submit) to these, chances are they will ask you to review eventually. And this is what the scientific community expects you to do, not to give credit to a publisher that has no interest in science whatsoever and just wants to collect as many 'article processing charges' as it can, quickly.
No!
Simply say "No, I'm too busy at the present time."
No one will be hurt or offended, and it is not like you'll be lying.