Does matter stacks up as it approaches Black hole? When something approaches Black hole it'll experience time dilation with respect to a frame away from the black hole.  
So to an observer away from the hole the object would seem to slow down until it finally appears to have stopped . 
Would that mean all the matter that is falling into Black hole since its birth would still be observable stacked on its surface to an observer from earth if he visits it?
 A: Yes and no. Remember in special relativity whenever someone asks a question, they always are told to draw a spacetime diagram. The same thing happens in general relativity. If you want to see what is possible, consider drawing a Carter-Penrose diagram.
For a black hole you can draw the event of a test particle crossing the event horizon. The past light cone of that event includes parts of the spacetime and not others. So anything outside that past light cone can't see that event without themselves crossing the horizon. And that event only sees the thing in the past light cone before it crosses.
When you stay outside, you only see the event on the outside. So if you have a black hole that formed by collapse you still see the center of the star, just from way back before the event horizon formed.
It will be slow, and it will be red. And if it is the center the outside of the star might block your view (just like for any star).
So, it is not stacked up on the outside. If you dug a mineshaft on your star and supported the sides then you'd still be able to look inside. The outside is only more visible since there isn't anything farther out to stand in your way.
The whole stat, center, medium layers, and outer layers. Is all red shifted, and you see the events from before the horizon formed. And you can see it except for how slow and red it is.
