I think your routine seems OK.
For running, it might be an idea to map out 50m, or 100m, or 200m (whatever)
stretch of decently level surface near your house where you can jog, run or sprint safely.
Just run back on forth on it. The idea behind the running is to improve the cardio and
also to condition the legs.
In the military, just doing push-ups or sit-ups and training to pass the CF Express
test isn't the point of military fitness. Often, you're called upon to move equipment,
go on ruck marches, stay up for work long periods of time, moving thru and over
obstacles, crawl into confined spaces, etc, and it takes overall fitness to keep
persevering.
A good overall-body weight program is good for strength (don't forget abs and lower
back for a stong core), some say pilates like program is good for flexibility, badminton/floor
hockey/sports for cross-training, running, and fast walking pace hikes will condition the
body for strength, endurance, and maintain conditioning.