If you have 401k from an employer does that count as health insurance coverage?

No.  A 401K is a retirement plan like an IRA.  Nothing to do with health ins.

No, a 401k is deferred compensation. It would be amounts that you put toward a retirement plan. Employers sometimes indicate an amount for health insurance in Box 12a W-2 with code DD. They will also issue you a Form 1095-C. Employer-Provided Health Insurance Offer and Coverage Insurance, provides you with information about the health coverage offered by your employer. In some cases, it may also provide information about whether you enrolled in this coverage.