Is it okay for me to put all my surplus comfortably in overnight funds? Do you think that it's as good as my bank account?
Yes, overnight funds by their very design could be a little safer than your savings bank account. Because if you are faced with a situation like at Yes Bank, money parked in overnight funds is unlikely to get stuck as it's invested in overnight instruments. So in that sense they could provide better diversification.
I would say that most individual investors will also be able to get moderately higher returns without assuming any meaningful risk even with most conservative liquid funds. Do not look for the highest-return-providing liquid fund, but a combination of liquid and overnight funds is reasonably safe.