system
Given the following post, respond as if you're commenting on Reddit:
human
How can we say that a black hole grows, if in our frame of reference, no matter actually falls past the event horizon?

I guess the title explains it all. I understand that matter that falls in the black hole experiences normal time so it would go past the horizon pretty quicky, but to the rest of the universe, matter never actually goes past the horizon. Or so I've heard. How can the black hole grow then?

Bonus question:

I have read that right before you go past the horizon, you can the rest of the universe sped up and blueshifted. How far into the future would you see? If you can see billions of years or even more time pass by, how does that fit in with the idea that black holes don't actually last forever, but evaporate over incredibly long times (the smaller ones go faster). Wouldn't the black hole evaporate before I could fall in?

This has been bugging me for so long now,  I hope to find some meaningful answers.
gpt
The black hole can grow just like any other massive object, there will just be a lot of stuff near the horizon when it is looked at from our reference frame. It doesn't really matter whether or not the horizon of the black hole is seen to grow from our frame of reference; if you wanted to go check it out by falling into the black hole, as you got closer to the horizon the time dilation effect would go away and you would see stuff falling into it and see that it has grown. Another thing to point out is that the horizon itself will move outward to "meet" the in-falling matter; it is not quite as simple as imagining a static horizon that only grows once the matter falls past it. 

Regarding black hole evaporation, if the black hole evaporates, then so will you, so you will not be there to "see" the evaporation. There is no paradox, because even though you see the rest of the universe sped up as you fall into the black hole, you will be evaporated before the end of the universe (ie very quickly, from your perspective). Note that evaporation is a quantum process, so we won't fully understand it until we have a fleshed-out theory of quantum gravity.