No, this is not correct. The "flip" is in a particular choice of coordinates, not in spacetime itself.
> time is traversable in either direction while the singularity becomes an inevitable place in the "future"
It is true that the singularity is inevitably in the future--that's because inside the horizon, the future "time" direction points towards the singularity. But time is still only traversable into the future; you can't "reverse" your travel in time inside the horizon.
However that doesn't mean you can't move when you cross the event horizon. You can do that like usual (except for gravity pulling you inside. You can. It only means outside observer won't be able to see what you're doing, because of the time dilation (and the event horizon of course).
This kinda implies time and space are the same thing, it just depends on your point of view. Still have to see about that :D
Neither of these things are true, and I have no idea how you are getting either of them from the Wikipedia article you linked to. Penrose-Terrell rotation, which affects how objects appear to observers when they are moving at relativistic speeds relative to those observers, does not "flip" the time or space axes; it's an optical effect due to the finite speed of light.
As I noted in another post upthread, the "flip" of time and space axes inside a black hole's horizon is a property of a particular choice of coordinates, not of spacetime itself.
> This kinda implies time and space are the same thing
No, they aren't, because there is still a fundamental difference between timelike and spacelike directions in spacetime. That is true regardless of how you choose coordinate axes.