1)The polarity of an electromagnet can be determined using the second right-hand rule.

Question

true.

2)Current passing through a conductor is increased from 10 A to 15 A. This decreases the strength of the magnetic field produced by the conductor.

false.

Answer 1

1) I m not familiar with which right hand rule is "second", but I found a web site that says:
<<The polarity of the electromagnet is determined by the direction the current. The north pole of the electromagnet is determined by using your right hand. Wrap your fingers around the coil in the same direction as the current is flowing (conventional current flows from + to -). The direction your thumb is pointing is the direction of the magnetic field, so north would come out of the electromagnet in the direction of your thumb.>>

2) True. Magnetic field strength is proportional current.