Once you enroll in Medicare (April 1, 2015), you are no longer eligible to contribute to an HSA. You can, however, contribute to an HSA for the months prior to this date (assuming you are covered by a high-deductible health plan for this period). Thus, you can contribute for one quarter of the year (and your dollar limit on your contribution is one fourth the annual contribution limit.
Generally, an unmarried person who maintains a household for dependents and is allowed to compute his or her tax based on head of household rates, which are more favorable than single person rates.