The types of speed workouts I've done are generic 200m, 300m, 400m intervals and I've done some 50m accelerations with a parachute.
I will start by suggesting that you get rid of the parachute. sell it to some kid who wants to make his own kites, or maybe find some science geek who's building a rocket that needs a parachute for re-entry purposes, but high school freshmen do not need a parachute for their 400m training. this is the track and field equivalent of a 5-year-old girl smearing her mom's make up on. "gimmick" isn't even close.
having got that out of the way, it isn't real clear from your post, but I think you want to improve your 400m speed specifically so that you can race the 800m and 1600m faster. I am in any event going to answer on that basis, so if I'm wrong, you'll have to say so.
to improve your basic 400m speed you need to do three things.
1. hit the gym and do some strength and conditioning work. you need especially to focus on the muscles of the core, abdomen, hips and thighs. especially hip flexors, adductors, glutes, and the structural muscles that support these. this does not necessarily mean lifting weights, there is a ton of stuff you can do before you need to start doing cleans and deadlifts, but if you haven't already, you should make a start. don't jump straight into a huge program of 5 sets of 20 reps of 20 exercises or something equally as stupid. start with low reps of 2 or 3 exercises and over a few months gradually build up a balanced program. either do a little bit every day, or a serious session twice a week, and that will be more than enough at your age.
2. work on good running posture. there is no point doing this until you have some muscles to work with. you cannot, for example, rotate your hips without good hip flexors and active glutes. so start with the gym work. when you start to notice an improvement, use those muscles to improve your posture. main point is to keep your hips in the correct alignment. think of your hip girdle as a bucket of water. you don't want it to tip forward so the water slops out the front, and you don't want it tipped back so water flops out the back, you want it level so that all the water stays in the bucket. one way of working on this is on a treadmill, but there are others, and you just need to try a few and see what works for you.
3. if you want to run faster, you have to run faster. after a warm up, run 6 - 8 x 60m sprints with a slow walk back to recover. start at around your 400m speed and as you work through the set try to make them a little sharper so that you close at around your best 200m speed. do not try to force these and do not under any circumstances try to "sprint." the point is to feel relaxed at this speed, focus on fast feet and fast hands. do not think about knee lift, this has nothing to do with what you are trying to achieve. after several weeks of this, alter the distance a little. go from 60m to 80m and work there for 6 - 8 weeks, then go to 90m for a few weeks then back down to 60m and so on. each time you change the distance you will feel a difference. do these without a parachute. it makes landing harder but it means you run faster, which is, after all, the point.
after you have been doing those for a few weeks, start on the 200m's. you do the above sprints first, then, after break of around 8 - 10 minutes while you do a lap of very easy jogging for recovery, you want to run a set of around 6 - 8 x 200m around 1 - 2 seconds faster than 800m pace. so for you that's 32 - 34 seconds, with a long walk recovery, around 2 - 3 minutes. gradually, over a couple of months, as you become adapted to them, and if you are recovering well, sleeping well, and injury free, increase the number to around 10 -12.
if you are going to be doing more than one type of training on the same day, do the fast track work (item 3 above) before regular intervals (instead of the 200m repeats). do intervals before doing gym type stuff (item 1 above) and do gym type stuff before doing other types of running (tempos, fartleks, etc). when you get into winter and you're doing hill sprints, they fit in where the fast track work goes, do them first.
this will take time, and it needs all three strands to be working together but with patience and consistency you will get faster.
the other stuff you do, the long runs, the tempos, the hill sprints and so forth, they are designed to incorporte this speed into your 800m and 1500m performance, so you will need to keep doing that just as you are. you will therefore have to make sure you take two days rest every single week. this is possibly the most important part of your training program so do not get tempted to cut the rest. rest and recovery is where you acquire the benefits you earned in your training.
cheers.