Filter design for an unusual EEG experiment
Is my filter &quot;reasonable&quot;?

I would say no. The time domain ringing time of your filter far exceeds the length of your signal, there isn't enough signal for the output to stabilize.

Can I do better?

Difficult to say. Filter design involves complicated tradeoffs between many different factors and the &quot;best&quot; really depends on the specific needs &amp; sensitivities of your application. You have partially explained what you want to do but not in enough details to give a recommendation. I'm skeptical about &quot;looking at the phase&quot; approach. Signal phase has only meaning if you have a well defined time reference for $t=0$, which most signals don't.

Can you recommend to me some learning materials for a filter design.

I personally like that one https://ccrma.stanford.edu/~jos/filters/ but I'm also mostly and audio guy.

(*) This is obviously cut from continuous EEG signal - can it be just cut (boxcar window),
or should I apply something different (eg. Hamming window)?

Depends a bit on your application details. Ideally your filter &quot;ringing&quot; is significantly shorter than your signal. Then you can just take a &quot;large&quot; chunk of signal, filter it and cut off the edges to remove the filter transients.

(*) Is my expectation justified?

Can't say without looking at your signal first. A sufficiently narrow band signal will look like an amplitude and/or phase modulated sine wave. However, if your original signal is very noise-like, you'd have to make it VERY narrow to look like that.