I'm pretty sure everybody can backdash out, or at least back dash safely. Before certain characters got punished by f23 for trying to back dash after breathe and that shouldn't be the case anymore. There are definitely characters that backdash but get stuck in pressure again(probably all the characters that got punished for backdashing before - Ares, Deathstroke, Lex, Raven, Doomsday, Green Lantern, Hawkgirl).
MB b3/f3 probably isn't universal. I haven't tested since the patch, but Ares used to be unable to MB B3. It'd get stuffed by the second hit of f23. I'm sure other characters have similar issue.
D1 is not universal. Bane can't d1. Ares d1 will whiff and he'll get punished. It may be possible to time it correctly with Ares so that the d1 will hit but it's difficult and you definitely can't just d1 the second you come out of blockstun. There may be others that don't work.
Edit: Ares is still unable to MB B3. As far as I know Ares only options are MB F3, pushblock, standing 1(trades or whiffs), or d1(usually whiffs). A backdash forces you to block the end of f23~breathe, MB b3 gets stuffed, and d1 is his only normal faster than 8 frames.