Asking 'why' too much in math and dont know when to stop. sorry if the question seems weirdly phrased.
For a long time, the way I have done math in general is to sometimes just accept things as they are. For example, Pythagoras Theorem states the way to find the hypotenuse of a right angle triangle. How (the proof or 'why' it works)? Doesn't matter, just do it and you find the answer. This has scaled up to my current position as a high school senior doing a-level maths, across various topics from trigonometry to graph theory to calculus. 
While I enjoy math, and am very good at it from conventional standards (getting A/A* predicted on tests, and breezing through the books), I constantly feel that I dont really know where it comes from. Yes, the basics are there (a circles chord when bisected passes through the centre, proof by standard pattern spots in integration, etc) but I always find myself asking WHY thats true. I get the answer in the end but I dont really know what I am doing. This problem really shows itself when I deal with abstract questions (or 'fun' questions) you find in olympiads and the like. The solutions seem so simple and I cant help but appreciate them but for whatever reason I can rarely do them. The way I tried to overcome this is by covering topics I had just accepted to always work and understand their core concepts. 
And this relates to my question. I cant stop myself from asking WHY that works. Eventually I just hit a wall where I am forced to accept certain things as facts (a right angle triangle in a semicircle ALWAYS has its base as the diameter, the determinant of a 2 by 2 matrix ALWAYS uses this particular formula). I want to get better at maths but I dont know when to ask why and push further or when to stop, accept it, and move on. Any advice? 
 A: Asking "why" is generally a good thing in mathematics. It leads you to think more deeply about results that other people might take for granted, and about the assumptions behind those results (which are often not stated explicitly).
To take your examples:
Why is the Pythagorean theorem true ? Well, there are various geometric proofs, but if you look at them carefully you find they all assume that we are working on a flat (or "Euclidean") plane. Suppose we draw a triangle on the surface of a sphere. Will the Pythagorean theorem still hold ? No. For a small right triangle on a sphere (small compared to the size of the sphere), its hypotenuse will be slightly longer than the value predicted by the Pythagorean theorem. This difference can be used to determine the size of a sphere (such as the Earth) from very accurately measuring the angles and sides of triangles on its surface - a process called geodesy.
Why is the angle in a semicircle always a right angle ? This is because the diagonals of a rectangle bisect one another. So why do they bisect one another ? This leads you to think about symmetry. Apart from a rectangle, what other polygons can be drawn so that all of their vertices lie on a circle ? If we are given the co-ordinates of the vertices of a general polygon, how can we tell if there is a circle that passes through all of them ?
Why is the determinant of a $2 \times 2$ matrix given by the formula $ad-bc$ ? Was this formula just picked at random ? No. If you draw a parellogram with vertices at $(0,0)$, $(a,b)$, $(c,d)$ (the rows of the matrix) and $(a+c,b+d)$ then you will find its area is $|ad-bc|$. If $(a,b)$ is parallel to $(c,d)$ then the parallelogram has area $0$, and so the determinant of the matrix is $0$. This also means that the linear transformation represented by the matrix squashes the whole plane down to one line, so it is not invertible. And this explains why a $2 \times 2$ matrix with a determinant of $0$ has no inverse - which is an important property.
I think you should keep on asking "why".
