Yes, it's possible to claim your mother if she wasn't married at the end of 2018, had no income other than Social Security, and received more than half of her support from you. There are no exemptions for dependents in 2018, but you could qualify for a non-refundable $500 Other Dependent Credit.
Your father, on the other hand, would be filing his final return as Married, Filing Separately. He won't be able to file as Single. Depending on his situation, it might be more advantageous to file a joint return with your mother.
If his return results in a refund, your mother could be able to receive it if she files Form 1310, Statement of Person Claiming Refund Due a Deceased Taxpayer, if she would otherwise have inherited your father's estate.
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