They will be safe even if broker is busted, make sure to update your details correctly so even if shares are moved in and out you will receive direct sms from depositories.
Ideally no, but in cases if your account is in debit for any reason then broker can to make good for the debit.
In any case he should not use but if broker go bust your idle money can go along with broker, so better be alert when choosing broker, Can check this to know how safe it is to choose Zerodha.