If you have an insured car and buy a second vehicle how long of a grace period is there before you need to add the second vehicle to your existing policy?

Check your policy. it will state it there. It differs from Co to Co.

It depends on the policy you have and the dealer you get it from. If your current insurance covers everything you drive, its covered. But if not, than the dealer may offer a 48 hour binder to cover you till you can get to your insurance company.