Gravitational waves also have frequency. And they have the same relationship between frequency and energy per particle that photons have. This is one of the reasons why it’s so difficult to detect gravitons: We expect that the highest-frequency gravitational waves found in the Universe would be in only the kilohertz range, which is a much lower frequency than one usually deals with in electromagnetism, and hence each individual graviton would have an extremely low energy.
They also have polarization, but it doesn’t work quite the same way as it does for electromagnetism. With electromagnetism, you can consider the two “basis polarizations” to be vertical and horizontal (i.e., with a 90º angle between them), and all other polarizations can be constructed by combining those two (with appropriate relative amplitudes and phase shift). In gravity, though, the two basis polarizations are + shaped and x shaped (i.e., with a 45º angle between them). Polarization of gravitational waves is very important, because all gravitational wave detectors that have been built are polarized, and have one polarization that they can’t detect at all.
You’re touching on what may be the most important unresolved question in theoretical physics: inconsistency between general relativity and quantum mechanics,
Einstein bashed his head against it for the last half of his life without success. As of now, we don’t have any good answers. String theory looked promising for a while, but it’s been 50 years now and it hasn’t really resolved anything.
The current situation: we just don’t have a good idea at the moment.
There’s a very great deal that we don’t know about the intersection between quantum mechanics and general relativity, but that doesn’t mean that we know absolutely nothing. Both of the OP’s questions are firmly in the realm of what we do know.
Oh, I should also mention a few more things about gravitational wave detection:
1: While the typical frequencies are far lower than typical frequencies of light waves, they’re similar to typical sound frequencies. You can, in fact, convert many gravitational wave signals to audible sound signals without shifting the frequency at all.
2: Also like sound, you can detect the frequencies with great detail. Colors, as perceived by the eye, are only an extremely crude approximation of the spectrum of a visible light source, but whenever you detect gravitational waves (or sound), you can pick out nearly all of the spectral information.
3: Also also like sound, gravitational wave detectors aren’t very directional. You’ll get the strongest detection in certain directions, and little or no detection in others, but you can’t pinpoint direction with a single detector any better than “over in that general vicinity (or maybe the exact opposite direction)”. You can (usually) do better with multiple detectors working together, though (just like you can better localize sounds with two ears than with one) (which is one of the reasons why most work with gravitational-wave detection is done with the three or four best detectors in the world all working together, rather than with just one of them).
The sound analogy isn’t perfect, though, since unlike both electromagnetic and gravitational waves, sound waves are longitudinal and hence not polarized.
