From fft result one can affirm that the signal is affected by white noise?
These are just some hints on how to proceed which are too long for a comment. We cannot give a definite answer from just looking at the plots.

First, you should plot the magnitude of the FFT in dB, i.e. plot(20*log10(fft(signal))). Then, you would not need to plot different zoomed versions.

To refer to question 1) Is this the whole signal or just a part of it? Try analyzing a longer measurement cycle to become more certain. Certainly, there is some addition of white noise to the signal. But, additionally, it seems to me there is an additional sine-wave of period length 4 contained (referring to your first plot). 

To do some more analysis: 


Assuming you measure a constant acceleration, remove the mean from the signal. Then, the remaining signal just contains the measurement error.
Have a look at the (circular) autocorrelation of this error. In case of white noise, it should be ideally a single peak at delay 0. If the autocorrelation exhibits extra (significant) peaks, there probably is something extra on top of the white noise. (Looking at your FFT-plots, I actually expect some extra peaks).


To answer questions 2), 3) (I dont really understand your question 2)):

If your sampling frequency is 56Hz, your FFT output will range from 0 to 56Hz, where the distance between the bins is 56Hz/FFT-length. Furthermore, as your input signal is real, the frequencies above 56/2Hz will be a mirror of the first half of the frequency domain output, they do not contain additional information. As a general rule for Fourier Analysis: The frequency resolution $\Delta_f$ after FFT is only determined by the time duration $T$ of the original signal, given by $\Delta_f=1/T$. You can have a look at this article I wrote on my website about the FFT and frequency domain resolution as an introduction to the topic.