Number of charts on specific manifolds I read somewhere that radial co-ordinates are not considered charts for n-spheres and that a minimum of n charts are required to map it properly. 
With regards to the suitability of radial co-ordinates as charts I have noted the following points:
-As the n-sphere has a pre-defined metric, there is already a definition of distance and 'closeness'.
-According to the book, due to discontinuities at some places (eg: the international date line in earth's case) and singularities at some points, radial co-ordinates are unsuitable.
-Perhaps I have not clearly understood, but don't the co-ordinate discontinuities and singularities arise due to the pre-defined metric on the n-sphere?
So from this can I conclude the following?
-To decide the minimum number of charts required to completely cover the manifold, we need a definition (like for the n-sphere).
-In this definition (for example x^2 + y^2 = a, in the case of a 1-sphere), we need to use an arbitrary co-ordinate system as a 'crutch'.
-Thus, to figure out the minimum required charts to cover the manifold (in manifolds like the n-sphere) we need to use an arbitrary co-ordinate system to first 'introduce' us to the manifold.
 A: 
a minimum of $n$ charts are required to map it properly.

This is false, unless there's a hidden requirement in "properly". Two charts suffice: stereographic projection from the North pole, and similar projection from the South pole.  

we need a definition (like for the n-sphere)

Yes, before we say anything about some object, we need to define it. For example: unit $n$-sphere is the set of unit vectors in $\mathbb R^{n+1}$ with the induced topology. 

we need to use an arbitrary co-ordinate system as a 'crutch'.

If we are defining a manifold in terms of a larger manifold containing it, having a coordinate system on that larger manifold certainly helps. We have to describe things in terms of other things we already know, and we all know $\mathbb R^{n+1}$ with its standard coordinates. 
That said, manifolds are not always defined by giving some equation, or set of equations in $\mathbb R^{n+1}$. For example, the sentence let $N$ be the tangent bundle of $S^2$ defines a four-dimensional manifold without referring to any Euclidean space containing it. 

don't the co-ordinate discontinuities and singularities arise due to the pre-defined metric on the n-sphere?

Well, if you put any other metric on the surface of Earth, we would still have the dateline, would not we? A sphere cannot be covered by a single chart because it's not diffeomorphic to any Euclidean space. In other words, it's because the sphere is not a boring flat manifold like a piece of a plane. This is not some deficiency of the spherical metric.
