It's not correct to think of mass as a "condensed form of energy." By Einstein's formula, [itex]E=mc^2[/itex], energy can be converted to mass and vice versa. Or, in other words, all mass is associated with some energy. Thus, objects with mass m, have an associated "rest energy" of mc^2. However, this is not the same as saying that mass is a "condensed form of energy."
It is also not correct to say that energy is a "condensed form of momentum." Even at the atomic level, energy and momentum are distinct concepts.
In relativity, energy and momentum are related, both being part of the energy momentum 4-vector, but, this does not mean that energy is "condensed momentum." That statement is nonsensical.
Condensed is a strange way of putting it. it refers to a lot of stuff in a small volume, but what is a lot and what is small?
I think the OP means to refer to intrinsic mass as being entirely a relativistic correction of some sort. In the case of a photon it turns out that the mass is only due to relative motion and the "rest" mass is zero. So the photon has mass, but it is really just energy. This is why physicists are careful to distinguish rest (or intrinsic) mass and relative mass.
So of course it is a common question to ask "Could the rest mass of particles like electrons really just be some hidden motion or aspect of space we don't understand."