We all know that light loses its energy when it is moving through expanding space and time. And sense a black hole can be summed up to a super compressed space time, shouldn't that mean that a photon gains energy when it enters a black hole because it is experiencing the opposite effect of the expansion of spacetime
From the perspective of an observer far from a mass:
Light gains energy (increasing in frequency) when it goes from farther away from a mass to closer to a mass. Energy is conserved: the increase in the energy per photon is equal to the decrease in gravitational potential energy caused by bringing the mass-energy of the photon closer to the mass-energy of the mass.
If the light subsequently gets farther away from the mass, the same relation holds, so the frequency goes back down.
These are gravitational blueshift and gravitational redshift respectively.
A black hole is just a special case; all masses exhibit this phenomenon.
So far as I know, it is unknown whether gravitational redshift and the cosmological redshift caused by the expansion of spacetime are one in the same. As a non-expert, I find the explanation compelling, since the universe expanding moves mass-energy (including photons) farther apart, and this must do work on the gravitational field.
Basically yes it does lose energy and it can not get it back. For your second qwestion well, we don’t know what happens in a black hole but we have general ideas of what happens in there and basically it’s just contrubiting energy into the black hole BUT a black hole could just be a incredibly different thing like a worm hole so you would have to be more specific with your qwestion