Are Christoffel Symbols Tensor?

It is important to note, however, the Christoffel symbol is not a tensor. Its elements do not transform like the elements of a tensor.

Are Christoffel symbols vectors?

Non-zero Christoffel symbols do not mean the manifold has curvature. All it means is that you are using a basis vector field that changes length and/or direction from point to point. A common example is polar coordinates on the plane.

What do Christoffel symbols represent?

The Christoffel symbols measure the degree to which an observer following a straight line in coordinate space is not in free fall. Such an observer, wanting Newton's second law to hold, would then have to introduce a force -- the force of gravity.