Is it ok for my 2 month old baby to sleep less than 15 hours? She slept through the night since midnight and woke up once or twice for dream feed, then stay awake till noon and slept for 2.5 hours only. Thereafter she is awake till now. I'm worried she is over stimulated and become fussy later. How do you put your baby to sleep?

It's totally okay. The average is literally that, an average. There will be some babies who sleep more and others who sleep less. When my LO was 2 months, he was sleeping even less than yours. Just make sure that you establish a proper bed time routine and she's in bed from about 7 or 8 pm at night. It's completely fine for her to be awake for most of the day.