Fourier series, Fourier transform for $f(t)=\cos{t}$ - amplitude spectrum vs. frequency spectrum vs. power density spectrum

Question

Let $f:\mathbb{R} \to \mathbb{R}$ be a function such that $f(t)=\cos{t}$ and $t \in \left[-\pi, \pi\right]$.

The associate Fourier series is computed using the following formula:

$$a_{0}=\frac{1}{2\pi}\int^{\pi}_{-\pi}{\cos(t)dt}=0$$

$$a_{n>1}=\int^{\pi}_{-\pi}{\cos(t)\cos(nt)}dt=-\frac{2n\sin(\pi n)}{n^2-1}=0$$

$$b_{n}=\int^{\pi}_{-\pi}{\cos(t)\sin(nt)}dt=0$$ The associate Fourier transform is computed using the following formula: $$F(z)=\frac{1}{\sqrt{2\pi}} \cdot \int^{\pi}_{-\pi}{f(t) \cdot e^{izt}dt}. $$ After computing, I obtained: $$F(z)=\sqrt{\frac{2}{\pi}} \cdot \frac{z \cdot \sin(z \pi)}{1-z^{2}}. $$

My questions are:

1. How can I obtain the Power Density Spectrum from Fourier Transform?

2. Which are the differences between amplitude spectrum, frequency spectrum and power density spectrum?

3. Can you recommend me some information regarding spectrum analysis for Fourier series and Fourier transform?

Thanks!