This is all good advice. Let me add...
Find out where your tests will be done. Most likely, it will be on a 400m high school track. As a non-runner training mostly on a treadmill, you just dial in a speed on the treadmill and forget about it.
On a track, YOU will have to set the pace by yourself. It. Is. Not. Easy.
You will have to do some workouts on a track to get a feel for pacing yourself outdoors.
Otherwise, you will most likely go out way too fast and burn out. So, do some workouts on a track.
You wrote that you ran "for 5:00 minutes straight at a 6.0 speed, then slowed down to 4.0 speed for two minutes, then back up to 6.0 for two minutes".
Here's a similar workout you can do once each week until your race. (Of course, you'll need different workouts on the other days.)
Run 3 minutes at 6.0 mph, slow to 2.0 mph and walk for 1 minute. Repeat that 5 times without stopping. This will give you 15 minutes at 6 mph and 19-20 minutes of aerobic time, but it won't beat you up as much as doing a hard nonstop run so you can recover enough to do an easy run the next day. Over 8 weeks, your progression would look like this.
Week 1: 5x 3min run / 1 min walk.
Week 2: 6x 3/1.
Week 3: 5x 4/1
Week 4: 6x4/1
Week 5: 5x5/1
Week 6: 6x5/1
Week 7: Repeat week 2 but at 6.5 mph for the run. Week 8: repeat week 8 at 6.5 mph
These workouts will build your endurance and help you get efficient running at your desired race pace.
To train for the 300m, you will need to go to a track. Warm up by jogging 10 minutes or so. Measure 30 meters. Take a running start and run the 30 meters as fast as you can. The first time you try this, you will feel yourself flailing around and wasting a lot of effort. That's normal. Try to run juuuust a little slower on the next one, but more under control. Do 4 reps. You will be sore the next day. Do this workout once a week for a month. After a month, you can replace this speed workout with 300m-specific workouts... two sets of 3x150m at 300m goal race pace might be a good first workout.
Ideally, you should have a long(er) run, an interval workout, the run/walk workouts I described earlier, and a couple of easy recovery runs each week.
Over the last month, you should do some race-specific workouts. Post back here and let us know your progress and we can recommend some other workouts for you.
By the way, you'll probably get some conflicting advice here. That doesn't mean that one person is necessarily wrong and the other is right. There is more than one way to reach your goal.
Oh, and also, there are a lot of immature posters on letsrun. Just do your best to ignore them. Good luck in your quest!