What nut measurement would match with these screws?

These are self tapping wood screws. If this gentleman wants to use a nut I would recommend a different type of screw

What is countersink angle of the heads on these screws?

I looked it up in Google and the most common angle is 82 degrees. Metric is 90. Remer 82 is the "most common " . So there are some other.. you could trace the angle on a piece of paper and actually measure it.

Are these threaded all the way to the head?

Yes, this kind of screw are all full threads and the screw length includes the head

Are these magnetic, stick to a magnet? thanks!

Dear customer, for the wood screws you inquiry, it might be a little magnetic. Actually 304 stainless steel (UNS S30400) is the most widely used austenitic chromium-nickel stainless steel. Its nominal composition is 18% chromium and 8% nickel, so it is also called 18/8 stainless steel. It is essentially non-magnetic when annealed and may become slightly magnetic when cold-worked. Hope that could help you. Have a nice day.