1. there are three spatial dimensions, which can be represented by x, y, and z axes on a graph. any other dimensions are a combination of x, y, and z. however, is there a particular reason why there can't be "diagonal" dimensions?

2.

3. There can be diagonal dimensions, and you can choose your frame of reference to have x, y, and z in any direction you want. You can also choose a polar coordinate system if you want. It all depends on what problem you want to solve. For most purposes, I think you will find that it is more useful to use the xyz coordinate system.

4. string theory predicts the existence of degrees of freedom which are usually described as extra dimensions - 10, 11, or 26 dimensions, depending on the specific theory and on the point of view

whether these are strictly speaking spatial dimensions is beyond me + it does become a bit hard to visualise

5. you can choose any three perpendicular lines to be your axis and their point of intersection to be the origin. i dont know if there is any specific reason for your question

6. you can choose any three perpendicular lines to be your axis and their point of intersection to be the origin.

Yes, and the three directions don't even have to be perpendicular. Such orthogonality has its advantages but is not even a requirement to describe 3D space. The three vectors, describing the three directions, must not be coplanar (in the same plane). If this condition is satisfied, each of the three directions is linearly independent of the other two, and you have a valid 3D coordinate system. It will be skewed in the general case, or orthogonal in the usually preferred special case. Take, for example, the three edges off the same corner point of a regular tetrahedron: They form a non-orthogonal 3D coordinate system.

7. Think of a man walking a tight rope. He can only move in one dimension either back or forward. Now think of a smaller organism on the tight tope such as a tiny fly. It can move in 2 dimensions, back or forwards (like the man) but it can also move around the circumference of the rope. although in this case the second dimension to the fly appears to be a closed-loop dimension.

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