It's funny, you sound like me when I was a teenager, especially noting the lines "I go through highs and lows" and "it's really hard to concentrate and I lose my train [of] thought easily."
You might want to get yourself checked out if this behavior starts interfering with your life. I wasn't diagnosed with bipolar disorder until I was already in college, though I can say with certainty that those symptoms (similar to yours) were manifest much earlier, approximately when I hit puberty. Of course, this is not referring to the first half of your post where you discuss open-ended philosophical problems; it's natural for people to think about the "big" problems in life and be subsequently overwhelmed by the vastness of it all and the insignificance of humans in the grand scheme of things. Rather, this is addressing the way that your train of thought naturally segued into the statement discussing how you go through these "highs and lows," indicating (to me at least) that the times when you wax philosophical is concurrent with changes in your mood. I should know, I'm exactly the same way.
Don't take this the wrong way, I'm not saying, "Go out, get diagnosed, and get medicated now" because frankly, not everyone responds well to medication and considering the state of psychiatric science throughout the past few decades, I frequently doubt the efficacy of modern drugs in addressing behavioral issues. Instead, I think it's important to recognize certain behavioral patterns in yourself in order to identify those particular thought patterns that eventually lead down the path of depression so that in the future, you can avoid those dangerous trains of thought and consciously alter your perspective into a more positive one (thereby dampening the inevitable depression period). Personally, I tried the medication route, didn't like it, and eventually settled into a routine of regular exercise and forced studying. If you're anything like me, I think you'll find that the concentration issue will lessen the more you force yourself to study-- like cardiovascular training, by pushing yourself to study and read at length, you'll gradually improve your mental endurance and ability to take in and process information.
Anyways, the mere fact that you're asking whether or not this type of behavior is "normal" means that you already know the answer to this question but are struggling to come to grips with it. Depending on your definition of "normal," I could say that, "Yes, it is normal for teenagers to go through periods of angst especially when trying to establish their identity as a person and that such thought processes often come hand in hand with the bigger philosophical problems of existence." Yet, I could also claim that since most people don't go through this period of angst, then statistically one might say that no it is not "normal" to think these things. Then again, one could also say that intelligence itself isn't "normal" either and so we can continuously establish various tautological propositions (see "No true Scotsman" fallacy) and run circles around a very simple answer to this question: do YOU think this is normal?
If you had to think about the answer to this question, then no, this is not normal behavior and you are not a "normal" person, at least when considering the larger sample size of the human population. Yet, like many things in life, not being normal does not equate with "abnormal" and as you get older, you'll realize that very very very very very few things are pure black and white. The vast majority of things/concepts/people in this world are measured in gradients between two extremes, drawn and toned in different shades of gray instead of the harsh, abrasive, clear-cut moral lines delineated by so many naive idealists.
The more important question from all of this is whether you can be happy with yourself in whatever it is you're doing. If philosophical inquiry isn't doing it for you (and from the tone of your post, I'm pretty sure this is the case), then find exactly what it is that will make you happy. When you do find that thing, that angst of yours will get moved to the backburner of your brain, with other more tangible problems taking precedence in your mind. That's called growing up.
