I can't recommend this book enough to help identify (and address) weak points.
First of all, kudos to you for zeroing in on two crucial form issues! I wish I'd done that at your age, instead of spending years developing bad habits that I had to unlearn!
Jay Dicharry talks about these exact two issues in Running Rewired. This is the best $20 you'll spend on a training book ever.
Your calf tightness could be a couple things, either needing to be loosened up with rolling (you can try a regular foam roller, a harder, knobby one called a Rumble Roller [what I use], or a lacrosse ball for pinpointing spots). Or, it may be your joints are too stiff, and you either need massage or stretching to increase range of motion. (He has diagnostics for these in the book).
Tight hip flexors were also a problem he diagnosed me with (very common with runners and people who sit down a lot). It's very simple, but not a quick solution: do a hip flexor stretch for 3 min per side, daily, for 10 weeks. That'll allow you to get your leg behind you more, which makes all the difference in efficiency, especially (as you've noticed) at faster speeds.
As you're already guessing, the other side of the coin is glute activation (another problem I had). There are lots of great resources on youtube for glute activation exercises, but a few that I've done hundreds or thousands of reps of are clamshells, glute bridges, and donkey kicks. (Note: concentrate on your form! Be patient with yourself, and even put a hand behind you to make sure you're squeezing that glute, and not cheating with your lower back and hamstrings, because that defeats the purpose.) Building new muscle memory takes time, but if you stick with it, you'll see major gains and be able to feel it in your stride. I sure have! I'm getting injured less and running faster than I was 5 years ago. :-)
P.S. for a quick intro to JD's work, check out this podcast: http://runningrogue.libsyn.com/episode-80-rewire-your-running-with-jay-dicharry