Your first paragraph is correct *as long as you're looking from far enough from the horizon*.
The second paragraph is incorrect. Locally, you are still in euclidean spacetime before, during, and after your crossing of the *event horizon*; this only becomes false as you approach the *singularity*.
Sure, if you're close to the horizon, people far away from the black hole do see you flat and redshifted, but you don't agree with them!
John Carlos Baez (npub1nf4…nqe4) Greg Egan (npub12cu…d38p)