ikalogic said:
1-If the input of a band pass filter is an oscilating signal (pulses) how is the output signal (in case the input frequency is not rejected?) is it a smoth DC signal? is it the same input signal but amplified?
a band pass filter will always output an AC signal. To really understand what's going to come out of it, you have to understand the concept of the frequency spectrum of a signal - any signal can be represented as a sum of sinusoidal waves of different frequencies, and the response of a filter to the actual signal is the same as the sum of the responses to all those sinusoidal waves (superposition) It probably isn't a concept you can just immediately understand, usually it's a sizeable chunk of an EE course in college.
Check out this page, which has a few (hopefully) helpful diagrams:
https://mathworld.wolfram.com/FourierSeries.html
You can find the response of the filter to any sinusoidal wave since you know the filter's frequency response (ie - the gain vs. frequency) Usually (though not necessarily), a bandpass filter will have close to unity gain in the passband and drop off outside the passband. The output of a bandpass filter to a sinusoidal signal of a given frequency is then going to just be the same sinusoidal signal, scaled by the gain of the filter at that frequency. If it's within the passband, the output should be pretty close to the input, if it's outside the passband it will be attenuated.
If you want to visualize the response due to a more complex signal, such as a square wave or series of pulses, you would probably want to take the fourier transform of the signal, which converts it to the frequency domain so you can see its frequency content, and see how that lines up with the filter response. However, just for an easier "getting a feel for it" analysis, designing a simple filter in some circuit simulation software and running some signals through it to look at the output is probably the best bet. For example, what you should expect if you put a square wave or a series of pulses with a certain frequency through a bandpass filter, is an AC signal that looks roughly like a sine wave at that same frequency, with a degree of distortion that depends on how good the filter is. If the filter were a perfect bandpass (completely rejected anything outside its passband, completely passed anything inside it... impossible to build one but useful to think about) then you would get a perfect sine wave, and if it's not a very good filter then it would probably look more like a smoother version of the input signal, with more rounded edges.
Edit: I grabbed a slide from an old project presentation of mine and attached it. The BLUE signal on the left is the input of the bandpass filter, and the signal on the right is the filtered output. The input signal is a bit more complicated than you're asking about, but the response of a square wave (such as the green signal which I've drawn on the left) would look similar.