The Universe expands according to the Hubble's law: velocity is proportional to distance. There must be some distance, therefore, at which the velocity reaches the speed of light. This defines the horizon. The Doppler shift is so huge that the length of waves becomes infinitely long: We can not see beyond that horizon. Is this correct?
On the other hand, when we look in the sky we look back in time. Since the Universe has finite age we can not see beyond some distance.
So these are two horizons. Are they related to each other?
a. correct
b. "finite age" needs to be pondered. you are assuming that time duration is the same for all observers, this is not so. If we could see the edge of the universe, we would see time zero. But at that time zero location, it is not time zero, that was 11 billion years ago. What we perceive as time clicking on a clock is as erronouse as the distance of one meter being the length of a meter stick. All depends on movement, relative position and velocity of the event and the observer.
Most of us get stuck on this, using our experience on earth watching cars drive by, no realizing in the universe wen we look at the car, it is not there, what we are seeing is a photograph of it billions of years ago, when it was there.