Two minutes standing in between sets is too much rest, 6-8 x 400 @ mile with 400 jog in between is a much better workout. Also, if you're a young male, you might not need to be training such strenuous workouts to break 6.
6 x 400 @ mile with a 400 jog or minute standing is probably all you need. Work on your 800 to gain speed and try to get it under 2:30! Endurance can come later.
Based off of those workouts, you can definitely break 6, I'd estimate 5:40 or better, but you'll get much better gains doing workouts with less reps and rest. Being at your current fitness, the best thing you can do though is to just race. You could reasonably cut 45 seconds off of your mile time if you just keep racing miles and 800s.
My first season of track I ran a 5:47 in the preseason time trial and started the season with a 12:40 3200m and a 2:28 800m. My coach was terrible, so solely through racing I got a 5:07 mile and 2:14 800m by the end of the season. You'll end up running in the 5:20s or 5:30s if you stick with it!