Can I open a demat account in the name of minor? Can a minor buy and sell share - delivery based? Can I minor apply for an IPO?

Yes, a minor can have a demat account provided he/she has a PAN card.

Buying delivery based shares isn't possible as a minor cannot have a trading account. This demat account is mainly used when you want to gift shares to the minor or in case of inheriting shares.

Your IPO query doesn't have a definite answer. Some companies allow minors to apply for their IPO and some don't. This is generally mentioned in the prospectus. Click here for a more detailed answer.