Define atomic number and atomic mass number under what conditions are two atoms different isotopes of the same element?

Atomic number is the number of protons in the element's nucleus.

The atomic mass number is the number of protons plus the number of neutrons in the nucleus.

Different isotopes have the same number of protons but different number of neutrons

Mass is the amount of matter in an object.  weight is the measurement of the pull of gravity on an object.  say for example, you travel to the moon which has a different gravitational field compared to the gravitational field of earth. (gravitational fields: earth = 1, moon = 0.165)  now when you are on the moon, the pull of gravity on you is different than on the earth. and as weight is the measurement of the pull of gravity on an object, that means yes, your weight can and will change on the moon.  however, on the moon, on earth or even on jupiter, the amount of mass inside of you remains the same. meaning your physical mass remains constant.  in conclusion it is possible for your weight to change as your mass remains constant. 

No. an alpha particle is a pair of protons and a pair of neutrons, i.e. a helium