Moving Average FIR filter coefficients
I read that the coefficients are always 1 for moving average so this is what I did - is that correct?

Technically no. For a moving average filter of length $N$ all the coefficients are $1/N$. In practice most people use $1$ for all coefficients and then scale the output with $1/N$ It gives the same result and it's typically more efficient, but if you were to look at the difference equation, the coefficients would show up as $1/N$

Moving average filters are symmetrical,

Depends a bit exactly how exactly you define symmetry. You can certainly time reverse it without changing anything.

have no L-th band filter,

I have no idea what you are mean by &quot;L-th band filter&quot;

and are single rate filters right?

The concepts of multi-rate and moving average are mostly orthogonal. You can use the together , individually or not all.