... What options do[es] each character have ... in battle.
Sorry for the lack of replies on everyone's part, but this is a very broad statement that would take pages and pages to touch the tip of the iceberg on!
If you're looking for something specifically like "Squigly's options vs pressure and her reversals" or "Good frame traps with Squigly" then it's a lot easier to help you but what you've described is pretty much "Entire neutral game with every character please help."
It's hard to offer help to a question like that.
I main squigly so from what i know about i she might be a little weak in ... footsies
except with c.MK and maybe c.HP with a seria cancel ready ... s.MK is too slow.
am I right in thinking this way?
In Skullgirls a lot of the characters won't have dangerously scary ground normals for long ranged poking. A lot of the footsies come from the air moves and air spacing game.
Squigly is pretty good at that game though!
Just try her jumping Heavy Punch, it's a very long ranged high and a good poke that controls a lot of space in front of you if you use it while falling.
Also Squigly's jumping Light Kick is a very very fast lethal air to air that converts into combos.
Squigly can move the screen around and place lock down orbs on anyone in just a handful of frames from using a charged Sing into the Battle Opera Super [QCB+KK]
So she's totally got some good tools for the footsies and neutral game especially paired with another good space controlling assist (Big Bands Brass H assist creates the popular, 'SquigBand' team)
But if you wanted to touch on anything else it's better to get your questions a bit more narrowed down so people can help you better.
Hopefully this at least gets the ball rolling for you though.