I was going to have you contact Apple using this link: Contact Support but they probably would have had you try Safe Mode anyway. It might have been a simple fix.
Contact Support and click through the options until you establish human contact (phone or chat). They might have some additional suggestions that may work.
If that does not resolve your concerns to your complete satisfaction, make an appointment at an Apple Store. If they can't fix it right there and then, I suggest you stand your ground and ask for a full and complete cash refund on the spot. Take the money and immediately buy a replacement.
The reason for that suggestion is that you shouldn't have these problems with a brand new Mac, and you shouldn't have to part with it for even a day or two while they figure out what's wrong. Also, if the problems still occur in Safe Mode it raises the possibility of defective hardware.
You have fourteen days from the date of purchase for a "no questions asked" refund so don't put it off longer than that.