Pardon my question but I am no astro-physicist.

If a black hole is a singularity, A.K.A. a single point in space-time which is infinitely small and which has an infinitely high density, can matter actually go "inside" a black hole?

My question is not if we can cross/go past the Event Horizon area, but rather what happens to the matter that crosses it?

Does the immense time dilation make it so that any matter that crosses the horizon actually freezes in space-time before even "touching" the singularity? (But that would only be for an external observer if I'm right?) Or is matter simply "crushed" into particles and molecules from the sheer strength of gravity?

I know I've asked like 3 questions in one, but if I had to pick the main question it would be this :

Can matter go inside a singularity?