Could you think of a black hole as a puncture in the space-time continuum ?

Potentially.

But that's not the only path it can take.

Think about it like you would a road.

Some lead to dead ends. Other lead right back around where you started and simply waste your time. Others lead to places you never imagined you could get at from there. And yet others may lead right around the corner. And as you said. Some may lead right into the ocean.

Yes, but where is it going?

More like a faulty valve or a slow puncture

Yes. That is an acceptable way of thinking of it.

Nope. They are a product of mass, and the blackness of a hole and the effects it has on spacetime isn't part of the black hole itself, simply an effect of the black hole's gravity.

No. I think of a Black Hole as nothing more than a Dead Star who's gravity is so huge, light can't escape.

Not even is it a hole.

More a boundary than a puncture.

No. They are simply the remnants of huge collapsed stars with enormous gravitational forces. That's it.

They are NOT holes, portals, or anything else. They do have a number of very unusual characteristics, but they have no mysterious other function or role.

The term "black hole" is unfortunate because people infer a lot about them that is simply not true.