I've seen all sorts of stuff on the more philosophical side of karate, such as:

1) karate is not about aggression it is about self defense

2) there's no such thing as a first strike in karate

3) karate is about bio energy and studying the mechanics of the human body

4) karate is about maintaining ones good health

5) karate is about being able to physically dominate another and making size of person not matter

And there are some more. What questions do you think are the most important questions that karate, and martial arts, tries to answer?

You are mixing up karate (the art) and karate-do (the "way", or "the whole", one's journey with karate).

Most schools and/or instructors weave spiritual (philosophical) teachings into their syllabus and training, this comprises the "-do" and is distinct from karate as an art. There can be a lot of commonality of the "-do" across styles but that's due to common sense and human nature (or common lineage). Teaching a particular style of karate does not stop the teacher putting their own personal spin on the "-do".

karate is not about aggression it is about self defense

Nope. In that sentence the word "aggression" should probably be replaced with the word "attack" - karate is about controlled aggression, the art teaches you the control. Strictly speaking karate is about beating your opponent and preserving your own safety. How a person becomes your opponent is a moot point, you need to beat him (or not be there Daniel-san).
The "-do" aspect teaches you to not have bountiful flows of uncontrolled aggression outside of when you need it - IOW we don't want people walking the street being all Kobra-Kai aggressive.

there's no such thing as a first strike in karate

Read literally that is just totally incorrect. I can defend myself the moment I believe my safety is in danger - that does not mean that I have to wait for someone to hit me first, I can certainly make the first strike if I need to.
The "-do" aspect actually means one should try to live one's life without causing conflict (the "first strike").

karate is about bio energy and studying the mechanics of the human body

"bio energy" sounds like one of those esoteric bunkum terms. "Mechanics of the body" is a "duh" statement, as in "Duh, well of course!". Body mechanics are heavily interwoven into the art, because it would be ineffectual without them.

karate is about maintaining ones good health

Another "duh" statement, except it has nothing to do with karate - it applies to life in general. Karate will have a beneficial impact on that goal, but will not be the sole reason for it. IOW, karate will contribute to your good health (ignoring injuries!), but it won't be the sole cause of your good health. Your pursuit of the "-do" aspect should also contribute to your good health.

karate is about being able to physically dominate another and making size of person not matter

This is not philosophical, it is motivational and/or technical. It means that size determines nothing except the techniques and approach you use. You should be good enough that you can use the art despite the characteristics of your opponent or your own characteristics. Karate is no magical equalizer in itself. A smaller person who knows karate will (should) have a better chance against a bigger person who doesn't know karate, but if that bigger person does know karate then the advantage changes again - it now becomes who knows the art better, who can apply the appropriate techniques better, who can achieve better positioning within the immediate environment, etc. The person who knows karate can still be beaten by one who doesn't - karate doesn't guarantee anything.