Heating the Gallium, and thus melting it, is easy.
Simple electrical resistance increases heat, and that can be done by either passing an electrical current in the opposite direction of a standing magnetic field, or rapidly pulsing alternating currents through a conductor.
With regards to Mercury.... I don't think that's the case.
We have liquid metal amalgums with super conducting properties that are composed of much heavier elements then mercury. If the atomic mass of mercury was what gave it the ability to produce gravitational effects, then we could reasonably expect to see similar effects produced by these other materials. If that was the case, I'm fairly certain we would have heard about it before Eugene Podkletnov.
I think Aluminum produces the antigravity effects that it does because of it's unstable electron configuration.
This is gonna be extremely technical... I wish spoiler tags worked here so people can skip this if they want to....
The Periodic Table of Elements is organized into families according to vertical columns, but, the thing that's not usually explained in chemistry class is that it's also organized into groups based on row.
Row dictates energy levels and atomic radii, Column dictates electron configuration and chemical activity.
The first row is composed of hydrogen and helium. At this level, there's only 1 type of path, or orbital, for the electron to follow in and around the nucleus. This path is known as the Sigma orbital. While electrons conform to a sigma orbital, one electron can stabilize another electron. for simplicity, let's say this is accomplished by allowing the electrons to rotate in opposite directions. Electrons always seek this stability. This is why hydrogen is so reactive. This orbital is denoted as s1
The second row has 2 types of orbitals and larger atomic radii. Again, elements have a Sigma Orbital, although at this point, it's considered to contain an exponentially greater amount of energy then the sigma orbital of the first row elements; this is denoted as s2.
The second orbital type is called a pi orbital. The pi orbital represents a higher energy state then the first sigma orbit, and less then the second sigma orbit. The pi orbital has 6 slots. Again, electrons stabilize each other by providing counter rotation to one another, but while in the pi orbit, they don't nuetralize each other immediately. Further muddying the waters (aside from hizenburg), is the fact that at a smaller atomic radius, sigma orbitals and pi orbitals can blend into each other, producing what is known as a hybrid orbital.
Okay... now... at this point we can look at boron (it has a similar electron configuration to aluminum, but with less potential energy stored in it's orbitals), and i can explain why aluminum has these effects:
Boron has a full sigma orbital and a single pi electron. Boron can't achieve a stable conformation because there's always an unbalanced electron, even if boron hybridizes. Aluminum has this same issue, but the instability is made worse because every thing is at a higher energy level.
To be fair... you might be able to use Scandium to generate a similar effect as aluminum as well, it just doesn't seem as pertinent because scandium doesn't resemble mercury at all.