After a gas is cooled to absolute zero it has zero volume. If you heat gas from absolute zero will it regain it's volume, or will it forever be stuck at zero? If it is forever stuck at zero, doesn't this defy to the Law of Conservation of Matter?

All real gases have molecules with non-zero volume, and they can only shrink to the point that the molecules are in contact, after which (before which in most cases, because intermolecular forces are not normally zero) they liquify. Helium has the lowest boiling point of any element because it has the smallest molecules (just one helium atom each) and the smallest intermolecular forces. Therefore, if we want to have an experimental model of an ideal gas at very low temperatues, we use helium.

For more on intermolecular forces and molecular size, see this answer and this one.

The reason we know the temperature of absolute zero, is that all gases behave more-or-less ideally over temperatures above their boiling point. We simply extrapolate the temperature-volume plot until we reach zero volume, and the temperature at that point is absolute zero.

Incidentally, to finish answering your question, if an ideal gas were cooled to absolute zero, then warmed, it would regain its volume. Remember, there are no intermolecular forces to hold its molecules together!