In fitness, you achieve results faster by focusing on one goal at a time. you wouldnt learn muay thai. boxing, kung fu, karate, and judo simultaneously right?
Work on your stamina first it will carry over into your future workouts..
You need to build all 3 energy systems, alactic, lactic. and aerobic.Thisll get you ready for a 90 min game.
alactic- do 3-7 sets of 10 sprints about 100 meters. add distance and sets over time.
lactic- do bodyweight workouts lasting 50-70 seconds
aerobic-sorry but if you dont want to jog you need to swim or at the least do a metcon workout day.
Build up pushups and functional workout
-simply shoot for adding a rep each week. Now that your energy system is better youll have more stamina.youll also be able to do more from your functional workout(see below)
unless you want to invest in a cheap set of bands, resistance bands, or that thin elastic band people use(all these are like 30 bucks for multiple sets! great deal) than use bodyweight full body workouts 3x a week
For a few weeks.. do one full body workout, then 2 workouts with extra chest exercises and less of everything else
Then do the same but with back exercises. this will help your pull ups in the long run. lots of latpulls and horizontal rows then do pull up negatives.
Now with your limited 30 minute window you may have to focus on 1 full body workout day that's 60 minutes and then do 2 30 minute workouts later that week. 30 minutes is not a lot for your goals unless you have a lot of time to slowly progress. Make sure your diet is in check too.. muscles or not.. you need them for pullups(you need back muscles to do this as well as strength) and muscular endurance so get ready to gain a little.