Glad you found her in time.
Indeed the wing is no issue, and likely caused from mating or even a bird attack - I've found several with missing limbs or wing issues in the wild.
I've done the same to old screens in the basement for my various bugs. The only problem though is aluminum can be rough on their feet/tarsi and can lead to broken ones, as the aluminum does not give any (no flexibility). I've even had a mantis that would occasionally get it's raptorial forearms stuck in aluminum screen trying to catch it's prey. The standard fiberglass/plastic screen works better for gripping, and without the mantis damage, if you can find a piece of that. Though the screen tends to be more of a problem for mantises nearly the end of their lifespans.
As your mantis is female she will be laying ooths soon (they lay ooths mated or not, but she is most likely mated), my Carolina's prefer to lay their ooths on the screen mesh between sticks. When she gets gravid (pregnant) and if she doesn't lay the ooth after a week or two, you may need to transfer her to a bigger container with more sticks so she can find a place to lay it. Some females are rather picky where they lay their ooths, and want more potential locations.
Regarding the container the height is good, but the width should be wider. The basic rule is the container should be 3 times taller than the length of the mantis, and 2 times wider then the mantis length. Which translates to 7" tall and 5" wide roughly, but adults don't need all the height as they will no longer molt, but I find more extra width essential for females to lay ooths.
As she is in a small jar with no cross ventilation, you should mist her twice a week (or every other day at most) with room temperature water. In this case, less is better, as it will prevent any mold problems, and mantises get their water needs from the prey they eat. A cheap $1 spray bottle will work great, just give it a few squirts - ideally you want the water to evaporate within 30 minutes or less once it is sprayed. So just adjust your watering amount until you find the right amount for her habitat.
Spring water is typically used for misting to prevent calcium deposits on the container sides; however, tap water should be fine it just may make the container dirty.
Heat wise 68F is a bit cold, but should be fine Carolina's aren't overly picky. If you want you can use a lamp with a incandescent bulb (anything not LED/fluorescent) to give her a bit more warmth during the day. Shoot for around 75F if you do give her heat, and she will be more active too.
Edit - Here is a
care sheet for Carolina mantises.
