Any progress is possible as long as you are dedicated and consistent with your workout. Personally, I improved a lot over a two week span so you can definitely improve over a month.
I'm male, but my weakness was running and the mile SUCKS. However, you have to dig deep and fight the urge to slow down. The first time I ran my mile during my practice CFA, I got a 9:34.
To improve my mile, I ran on a treadmill every other day for two weeks straight. I ran half a mile at a 7 minute pace and then walked .1 mile. (the treadmill gives you a semi-accurate distance). I then repeated this 6 times. Once I finished repeating that 6 times, that was the end of my running for the day. I noticed that every day that I ran, I became less tired and had more endurance and stamina. I noticed improvement and on my official CFA I ran my mile at a 7:13. That's significant improvement over my original mile time. If I can do it, I am confident that you can. One thing I did to keep me from walking or slowing down was legit YELL at myself during my run. I would yell out loud "LETS GO. PUSH IT. LETS GO LETS GO." or "You want to go to Air Force running like this? PUSH IT". Motivation can only come from yourself. I found that yelling out loud and being verbal pushed me to go harder and farther.
For the shuttle run, you just need to practice it. I ran the shuttle run on the days where I wasn't doing my treadmill runs. I had my dad time me and I just ran the event. I got used to the transitions and I learned how to keep my momentum going during my turns. The worst mistake you can do during the shuttle run is lose your kinetic energy. This will slow you down and result in a higher time. There are videos on YouTube on specific techniques that I would reference.
Another area I think you can improve in is your BB throw. To get good at the BB throw you really just have to practice the movement. I play varsity water polo so throwing the BB from my knees wasn't too bad (during water polo we throw the ball just using our upper body). It is a similar concept for the BB throw. Make sure to use your core when you throw and snap forward at the waist. Another tip is to generate momentum before you throw. Move your arms around with the ball before you throw. "Pump throw" before you actually throw. The more energy and movement you have before you throw it, the more likely it is to go further. If you have trouble gripping the ball, I would bend your hand towards you forearm and sort of cup the ball. This should provide a more stability. There are plenty of videos on YouTube on how to improve your BB throw.
Sit-ups are fine and the pushups may be fine. Not too sure. I would definitely try to increase your pushup rep by 5 just to ensure that it is a pass.
I hope this helps.
