So they say the remote observer will never see anything fallen to the black hole, because any object will slow down as it gets closer to the event horizon and eventually stop to stay there forever. Am I getting it right so far? With this said, it turns out nothing has fallen to the black hole up till now. That is for us, as remote observers, anything that ever tried to reach the black hole got stuck at its event horizon. So we can go and see it right away - it must be still there. At the same time they say that the black hole keeps sucking matter. So question is, to a remote observer, how does all this matter fit the event horizon provided it will never fall through it?
A remote observer will see the matter pile up at the event horizon so the density of matter there increases (to infinity if you wait long enough).
The matter falling into a black hole question has been discussed many times on this site, so I won't go into more detail here. However it's worth emphasising that you need to separate formation of a black hole from subsequent growth of the black hole. When you form a black hole by compressing e.g. a ball of gas, the event horizon doesn't form at the centre then grow outwards. It forms on the outside once the density of the gas is high enough. This is because the average density of black holes decreases as the mass of the black hole increases. It's easier to make big black holes than small ones.
Once you formed your black hole it's true that observers outside the horizon will never see anything cross the horizon. But this is no different from saying that those same observers see a continuously accelerating rocket slow as it approaches the speed of light. If you're on the rocket, or falling into the black hole, your experience would be different.