Antimatter just has the opposite electrical charge. It doesn't do anything weird at all with gravity.
Are there other types of Antimatter that focus on different properties?
We don't know that. It may have the regular charge but after computing the force it may experience the opposite behavior via F=ma since the mass is negative.
We don't really know if the charge is opposite or the mass. Blindly using the equations you may get similar results depending where you stick the negative.
Also, I seem to recall Dirac predicting the existence of antimatter because some solution to an equation had an m^2 term and when you take a square root to solve for m there are two solutions. Then the positron came along and this was forgotten and people just assumed it had positive charge rather than negative mass.
Both theory and experimental validation. Their interaction with electric fields, their interaction with gravity, conservation laws, and so on.
Here is a contrived example calculating a hypothetical quantity X = m * Y.
Suppose we observe that X is always negative.
By your logic, we would then assume that Y is always negative.
This is true if m is never negative, but it is somewhat possible that we would eventually find a situation where m is negative and Y is positive.
In a given interaction, charge is always conserved. So we see interactions where an electron and a positron collide they produce a chargeless photon. So it must have the opposite charge to an electron
Is there energy in an electric field? If so it must be signed or it wouldn't cancel out.
The energy contained in the electromagnetic field is nonnegative: as I understand it, within a given volume, it's simply the sum of the photon energy of all of the photons.
Meanwhile, electrons and positrons exist in their own particle field, and have both positive mass energy and nonnegative kinetic energy. When an electron and positron annihilate and produce photons, they convert their combined mass energy into kinetic energy in the photons. The only thing that gets "canceled out" is the positive and negative electric charge.