My first point, don't take me wrong, but you can post these either on matchup thread or in the general discussion
What could help you is to watch games, you have the archives from EVO where KDZ won the Injustice tournament and you have loads of stuff to 'eat, feast and digest'. You can learn a lot by watching games and taking notes, I like to do that.
Now, onto your points, if they are jumping alot you can either d2 or use his air grab to put them in check. Batman has a great j2, good air to air, cross up and jump in. If he's jump happy you can also try to dash under him and try to punish or to get some breathing room. Injustice has a great training mode, you can make use of that by recreating the same situations you encounter and have trouble dealing with. By doing that you'll learn great stuff about your character and some matchup knowledge.
Regarding Green Lantern, again training mode helps and you can check the framedata of Green Lanterns moves/specials to see what can you punish and which moves do you have to punish a certain move. (Check this, its the Injustice Wiki from TYM, it contains the framedata for every character, including DLC:
http://testyourmight.com/wiki/index.php/Injustice:_Gods_Among_Us) If you have trouble reading frame data we can help you with that.
Yeah the lift(Lanterns Might db1) from Green Lantern is usually followed up after b13, just block it he can't do much after you block the 'Lift'(that's what we called it around here) and if the frame data is correct from the wiki it's -26 on block, so thats highly punishable. Once more, hit the training mode and record Green Lantern doing b13 xx db1, then Playback and block the full string and see what can you do responding to that.
Superman, correct me if I'm wrong, isn't a character with many mixup options, he has a rather straightforward gameplay, but he has some tools to mix you up though. For example, say your oponent blocks a f23 breath, you can go again with a f23, but the second time instead of going for another breath, go for a scoop df1, a low instead of a mid. You can also go for a f2d1, a string that ends with a low. Even after f23 breath you can go for a MB b/f3 to beat attemps of poking from the opponent. These are some options to keep your oponent guessing and lead to guaranteed damage.
Well, you have options to anti-air jumping opponents it's just a matter to see the ones best suited for each jump. To deal with characters getting in Heat Zap(db3) and with Heat Vision(db1) to keep them at bay and you can respond with their attemps to deal with it.
On wakeup d2 isn't a good option, you can react with a wakeup depending of what the opponent's doing, if he's jumping try a MB/regular Rising Grab(db2) or just block, as blocking is generaly the best option. The wakeup window is a bit 'odd' to get used to if you are familiar with 'easier to see' wakeup windows like SSF4, it's a matter of habit to be honest.
Regarding his air normals I can't really give an input on that, since I don't know Superman that well, but his j2 is good for cross ups and you can use it with your air dash, which is a great movement tool, make sure to use it.
Your punishing options will revolve around f23, since it's a string that starts in 8f and the damage it leads...well it's damned great!
I hope I covered your questions and if anyone has better input, please help me out hehe
Injustice has a neutral game that it's not easy to get used to if you come from like SSF4, this is my case, so just practice, go to the lab, practice online and you'll get into it
