Translation:My mother is swimming.
Y meri instead of mere
मेरी is the feminine form and is used because माँ is feminine.
Can i say " meri maa theirthy hai"
It's a different tense.
मेरी माँ तैर रही हैं = My mother is swimming - Present continuous tense
मेरी माँ तैरती हैं = My mother swims - Simple present tense