Is it necessary to send my 2-year old to preschool now Or should I wait and directly send her to nursery at age 3 years?

I do not think it's necessary at all to send her to pre-school. The other day, I was talking to a friend of mine, and she said that the main reason I send my 2 and a half year old daughter to pre-school is so that she can develop social skills. She can be with other children, know how to behave when she is with so many around and develops sharing and since, they would be eating together at lunch time, she learns to eat everything that is on the table. So, if that's your reason, it is fair enough, but if it's to learn reading and writing, do not, as she would anyway learn that sooner or later.