Assuming that the person qualifies for the maximum rate of payment, the Widows (contributory) and the State (Contributory) are the same for persons aged 66 or over (currently 230.30pw).
If the woman qualified for Widow's Contributory Pension based on her late husband's PRSI record rather than her own, she may not qualify for the State Pension as it is based on her own PRSI record.
She can apply for the Household Benefits package at age 66 while remaining on the Widow's Pension.
She can apply for a medical card at any time. It is means-tested up to age 70.