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its mass will increase by an amount too small to measure directly

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Q: A metallic coin is given a negative electric charge How does its mass change?
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What is proton electric charge?

A proton has a positive electrical charge and an electron has a negative electrical charge.

When determining an electric field must a positive test charge be used or would a negative one do as well?

We could just as well use a negative test charge to determine an electric field, but then the Electric field vector would point opposite the direction of the force on the test charge.

What is the part of the atom that carries no electric charge?

The neutrons are the part of the atom that carry no electric charge. They are found in the nucleus. the protons carry a positive charge and the electrons carry a negative charge.

Is an electric charge a property of just electricity or is charge a property of all atoms?

Atoms contain both positive (protons) and negative (electrons) electric charges. But in the vast majority of atoms these positive and negative electric charges balance, canceling and resulting in zero total electric charge. When electrons detach from atoms we generate electricity. Where there are fewer electrons there is a positive charge. Where there are more electrons there is a negative charge. When two places have different charges we get an electric voltage. When electrons flow from a negatively charged place to a positively charged place we get an electric current.

The electric field of a point charge always points away from the charge?

If the given point charge is of positive one then the field points away from the charge. This is because we define the field at a point as the FORCE acting on unit POSITIVE charge. Like charges have to repel and hence the direction. If, other wise, the point charge is negative then electric field due to this negative charge would be towards the negative and not away from it.