fft - Interpolation and harmonics

A real valued causal sequence $x1[n]$ exists with length of the sequence being $N$. Valid indices of x conform to $0 \le n \le N-1 $

The DFT of x[n] is: $$ X1[k] = \sum_{n=0}^{N-1} x1[n].e^{-j.2.\pi.k.n/N} $$

The normalized frequency spectrum exists from 0 to $2\pi$. This frequency spectrum contains discrete frequencies which are integer factors of $\frac{2 \pi}{N}$.

A properly sampled signal fulfilling Nyquist criteria will have the valid range of normalized frequencies from $0$ through $(\frac{N}{2} - 1)$ $\frac{2\pi}{N} $.

As an example, for N=8, the valid frequencies are $0$, $2\pi.n/N$, $4\pi.n/N$ and $6\pi.n/N$.

When $x1[n]$ is upsampled with a factor of 2, we essentially insert a $0$ after each sample. This creates a new sequence $x2[n]$ with a length of $2N$.

The DFT of this new sequence will now be: $$ X2[k] = \sum_{n=0}^{2N-1} x2[n].e^{-j.\pi.k.n/N} $$

The discrete frequencies of this new sequence are $0$, $\pi.n/N$, $2\pi.n/N$, $3\pi.n/N$, $4\pi.n/N$, $5\pi.n/N$, $6\pi.n/N$, $7\pi.n/N$ and so on.

So it is clear that each new sample that was added to $x1[n]$ has introduced a new frequency component.

I have two questions now:

1. 
   

   As the harmonics (as the math seems to suggest) lies amongst the desired frequencies (e.g., $\pi.n/N$ is less than $2\pi.n/N$, and $3\pi.n/N$ is less than $4\pi.n/N$), shouldn't the interpolation filter be a comb filter?

   
   


2. 
   

   When I take a FFT of $x2[n]$, I expect to see the harmonics in the original pass-band. But instead, the frequency spectrum of x1[n] has been replicated.

   
   

What have I misunderstood?