1. Cross-up potential:
After ending the combo with d3 I tested to see if BA's jump attacks would cross-up even if opponent is holding back to block. Obviously, characters with slow walkspeeds are easier to cross-up and characters with fast walkspeeds have an easier time avoiding them.
Aquaman (all hit front)
Ares (j1 crosses-up, j2 hits front, j3 whiffs)
Bane (all hit front)
Batman (all hit front)
Black Adam (all hit front)
Catwoman (all cross-up)
Cyborg (j1/j2 hit front, j3 whiffs)
Deathstroke (all hit front, j1 lands behind)
Doomsday (all hit front)
Flash (j1/j2 hit front, j3 whiffs)
Green Arrow (all hit front)
Green Lantern (all hit front)
Grundy (all hit front)
Harley Quinn (all hit front)
Hawkgirl (j1 crosses-up, j2/j3 hit front)
Joker (all hit front)
Killer Frost (j1 hits front but lands behind, j3 crosses-up)
Lex Luthor (all hit front)
Nightwing (j1/j2 crosses-up, j3 whiffs)
Raven (all hit front)
Shazam (all hit front)
Sinestro (all hit front)
Superman (all hit front)
Wonder Woman (all hit front)
Again, this is taking into consideration that the opponent will walk back and not crouch or stand there. If the opponent crouches for a second before holding back to block then there's a good chance you will cross-up regardless of their walkspeed.
Just remember that a raw D3 has more frame advantage and that changes things quite a bit.
Cross-up potential of a raw d3 (pointblank):
Aquaman (j2 crosses-up, j1/j3 whiffs)
Ares (j2 crosses-up, j1/j3 whiffs)
Bane (j1/j2 hit front, j3 crosses-up)
Batman (j1/j2 crosses-up)
Black Adam (all hit front)
Catwoman (all cross-up)
Cyborg (all hit front but j1 lands behind)
Doomsday (all hit front)
Deathstroke (j1/j3 crosses-up, j2 hits front)
Flash (j1 crosses up)
Green Arrow (j1/j2 hit front, j3 crosses-up)
Grundy (all hit front)
Harley Quinn (j1/j2 crosses-up, j3 whiffs)
Hawkgirl (j2 crosses-up, j1/j3 whiffs)
Joker (j2 crosses-up, j1/j3 whiffs)
Killer Frost (j1/j2 crosses-up)
Lex Luthor (all cross-up)
Nightwing (j1/j2 cross-up)
Raven (all hit front)
Shazam (j1/j2 crosses-up, j3 whiffs)
Green Lantern (j1/j2 crosses-up, j3 whiffs)
Sinestro (all hit front)
Superman (j2 crosses-up, j1/j3 whiffs)
Wonder Woman (j2 crosses-up, j1/j3 whiffs)
Keep in mind you can always cancel your cross-up with MB close Boot Stomp or do ambiguous dive kicks after j2/j3 are blocked. Or even use far Boot Stomp to ass out in some cases.
2. Chasing the Backdash:
It's possible to chase/whiff punish certain backdashes a number of different ways. I tested these on the whole cast to know which backdashes can be 100% punished and which ones are safe after this particular knockdown (though the spacing and frame advantage is what really matters here, not the knockdown itself).
j2/j3: Ares, Doomsday (late/hard), Flash, Green Lantern (*not recommended because of Lift), Hawkgirl (*not recommended because of Wing Evade), Joker, Killer Frost, Lex, Raven, Sinestro.
EDIT: It seems the Lightning Storm ender has a little less cross-up potential but allows BA to punish more backdashes with j1/j3 (e.g. Catwoman). Definitely need to test that more.
Can't punish their backdash with j2/j3: Aquaman, Bane, Batman, Black Adam, Catwoman, Cyborg, Deathstroke, Harley Quinn, Green Arrow, Grundy, Nightwing, Shazam, Superman, Wonder Woman.
Dash, b23: Aquaman, Ares, Deathstroke, Doomsday, Flash, Green Arrow, Green Lantern, Grundy, Harley Quin, Hawkgirl, Joker, Killer Frost, Lex Luthor (b2 will whiff but 3 will hit), Nightwing, Raven, Wonder Woman.
Can't chase with dash b23 (best backdashes in the game): Bane, Batman, Black Adam, Catwoman, Cyborg, Shazam, Sinestro, Superman.
edit: I need to test again to know which backdashes avoid b2 completely and which ones just manage to block in time.
Black Magic, MB Lightning Strike & MB Lightning Storm: Universal (beats all backdashes)
Using Black Magic and Lightning Strike at this range is risky and obviously loses to most wake up attacks. That's why I only recommend doing these after having conditioned the opponent, after having established the fear of whiff punishment.
Interesting finds:
-Aquaman (storm and black magic > from the deep)
-Ares (storm > god smack)
-Bane (storm > command grab, loses to uppercut. black magic > uppercut, loses to command grab)
-Black Adam (frame advantage so storm > storm. Note: fj2 beats cage from here)
-Catwoman (storm > non-MB catdash)
-Doomsday (storm > venom, trades with upward venom)
-Green Arrow (storm loses to retreat arrow, retreat arrow loses to black magic/strike)
-Raven (storm is faster than all her projectiles)
-Shazam (storm > atlas torpedo and command grab)
-Sinestro (only fearblast is a threat from here but its whiff punishable on crouch with b23)
-Wonder Woman (black magic > amazonian uppercut and lasso grab, trades with tiara)
Especially unsafe vs Aquaman, Batman, Deathstroke, Flash, Green Arrow, Harley Quin, Joker, Killer Frost, Lex Luthor, Nightwing, Superman...
I would only try these on characters with great backdashes. Because otherwise if you think they are going to backdash why settle for 18-19% when you can full punish with j2 or dash b23 for 30-40%?
3. Dash Blocking:
There were only 2 characters in the game with specials too fast to block: Lex Luthor and Deathstroke.
Notes on Lex Luthor: Corp Charge is too fast. From this range BA can't backdash safely. Jump back j2 and block punish (b1 xx black magic or d2) are the only options to punish this meterless.
Notes on Deathstroke: Sword Flip is too fast. Block punish (b1 xx black magic or b23) or backdash d3 or backdash MB b3 or backdash, back jump MB Far Boot Stomp to punish.
A few random notes for personal reference:
-Doomsday (venom blocked, 11/d2 punishable. upward venom blocked, b23 punishable)
-Flash (charge blocked, b23 punishable. uppercut whiffs -punish?)
-Green Lantern (lift blocked, b23 punishable)
-Nightwing (staff spin blocked, flying grayson whiffs -punish?)
-Raven (singularity and event horizon blocked, d2 punishable. soul crush blocked, 22 punishable)
-Superman (rising grab and low scoop blocked, d1 punishable)