Yes, you can.
no
Small magnets should be fine, industrial strength magnets may cause problems in the cockpit
Theoretically, an airplane does not need to have any magnets in it, but most airplanes do contain magnets. Every electrical motor contains magnets, and small electric motors are used in various parts of an airplane, such as for raising and lowering the landing gear.
YES you can bring them
No
Yes
no but you can bring your own
Yes
no
Yes you can.
no
yes