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?

Personally I don't think it is necessary to send your kid to play school. It is a concept made popular in the last 10 years only. For my kids too I was not in favour of playschool but the only reason I put them there was that they learn to stay away from mommy for a couple of hours and they learn social skills.They get a change in surrounding and with more children their age they feel comfortable.