Don't listen to all the fear mongers. No your account won't get canceled, yes you might be called in for a KYC interview or updated ID. I've had my account with SCB for 15 years opened up on a tourist visa and the same with my Bangkok bank account only opened up a year ago on a work permit, and now I'm on a DTV. Neither branch manager told me to worry about anything they're looking for criminals.
Leaving is better than the option of an in-country extension and the 0.4 meters of paperwork that will be requested. Regardless, you'd have to leave after 360 days anyway.
elaborating a bit on Andy's reply yes you'll have to show proof of parental rights/birth certificates over the dependents just like you will show proof of being a legal spouse for your spouse's application
KL is not a good place to apply. A bit of a nightmare actually, they continually make requests for documents and 6 month leases. Use the group search tool Kuala Lumpur and decide for yourself
While children under 15 can't be fined and under 17 can't be banned for overstay, it's still the law that you need to enter on a Visa. It doesn't have to be the same Visa as the parents.