I’m a single parent with a high-deductible health plan (HDHP) coverage but have a child/relative that can be claimed as a dependent for tax purposes, and this dependent also has non-HDHP coverage. Am I still eligible for an HSA?

Yes, you are still eligible for an HSA. Your dependent’s non-HDHP coverage does not affect your eligibility, even if they are covered by your HDHP. You can contribute up to the statutory limit.