It is just as likely that the matter counterpart will fall in and the anti-matter escape.
In Special Relativity, light always travels at the same speed and that speed is c. In order to apply SR, you need to have an inertial reference frame. That means if you are near a gravitational field, you must cancel it out with acceleration – you must be in free fall. If you are falling through the event horizon, the light hovering there is traveling at c relative to you. In order to describe what happens as observed by a reference frame that is not free falling, we need to apply General Relativity. In GR, as in SR, nothing can travel faster than light, but light need not travel at c. The event horizon can be described in GR and light does stand still at the horizon.
Yes, you have to be careful about terms, any kind of particle can be cretaed by Hawking rdaiation, the only linmitng factor being that it follows a blackbody spectrum. However the particle that is emitted by the balck hole will always have postive energy while it’s partner will effectively have negative energy (that is to say Hawking radiation represents a negative energy flux across the event horizon) as it will be inside a potential well.
In general relativity light travels at c locally, however due to the curvature of spacetime the co-ordiante speed of light may be less than c.
It loses energy anyway, and when light loses energy its wavelength changes. The ability of gravity to do this has been documented IIRC; it’s called gravitational redshift or something like that.
As for the path of light and the curvature of space, it helps to use Einstein’s rubber sheet metaphor, in which the universe is represented as a rubber sheet where objects that have mass create a dimple. In the case of a black hole, the singularity produces an infinitely long funnel which, if at any point the walls become vertical, the light following a straight line will circle the walls of the funnel indefinitely.
It happens all the time and not only in black holes. If you move from relativity to quantum physics, you see that light is made up of “photons”. I’m not going to get into what they are exactly, but thnk of them as little pieces of light.
Now, one thing physicists love doing is taking tiny particles and running them into each other like a kid playing with Matchbox cars. Instead of breaking the die-cast bumpers off, though, what happens is that the tiny particles often turn into other kinds of particles. One common product is photons: mass turning into light. Sometimes two photons running away from the wreckage bump into each other and this crash makes more particles: light turning into mass.
Lest you think this sort of thing only happens when physicists play around, the current theory is that exactly this sort of thing is going on all around us all the time. Even “empty” space is positively boiling with particles popping into and out of existance and changing into each other while they’re around.