Why is it mere and not mera dada?
As a way of showing respect, words associated with people older than you (like दादा) or in a position of authority are conjugated as if they were plural.
Why not आयेंगी?
That's the feminine plural (or respectful) form.
Eg: मेरी दादी दिल्ली आयेंगी - My grandmother will come to Delhi