• What is the usefullness of Amperes Law?Does Ampere's Law only tell me something about the B field from a particular source?

Ampere's law holds for every distribution of currents (this form holds for static currents)

$$ \oint_{\partial \Sigma} \mathbf{B} \cdot \mathrm{d}\boldsymbol{\ell} =\mu_0 \int_{\Sigma} \mathbf{J} \cdot \mathrm{d}\mathbf{S} $$

In general, it is not a tool for direct calculation of the magnetic field , but we can use it in some (following) cases to find the field directly.

In all cases , where we can use it to determine the magnetic field, we find a (family of) path(s) , on which $\mathbf{B}$ is constant , and so comes out of the integral . This is the case when we find the field of a wire.

But suppose you want to find the field of two parallel wires. In this case you can not use this Integral relation as easy (and naively) as before , because the field is not constant on a simple path. In such cases we actually use the linearity of Maxwell equations: $$ \mathbf{J}_1 \to\mathbf{B}_1$$ $$ \mathbf{J}_2 \to\mathbf{B}_2$$ $$ \mathbf{J}_1 + \mathbf{J}_2 \to\mathbf{B}_1 +\mathbf{B}_2$$

so we consider one wire at a time and find the field of that wire, which simply can be found by choosing a circle surrounding the wire as our integration path. Then the total field will be sum of two fields.

Using these arguments , the field in a coaxial cable (your second problem) is $ \frac{\mu_0 I}{2\pi r} $.