How to determine the frequency of a waveform?
Question 1: the sampling frequency would be $64$ Hertz 
Question 2: the frequency indices range from $0$ to $63$


In the following code, I tried to mimic your data. At each run, a different observation is produced, based on a sine with a different amplitude distortion and offset. 

Using the FFTR.m code that displays one half of the spectrum for real signals, and removing the average, you can get the following figure:



% Simulated data to mimic your signal
timeSamp = 1/64;
nSample = 64;
xAxis = linspace(0,1,nSample)';
dataClean = sin(2*pi*xAxis*6);
distAmpl = 1/10*( medfilt1(rand(nSample,1),3)+0.15);
dataDist = data.*distAmpl + 0.01*(rand+10);

% Half-axis FFT for a real signal
 [fftR,fftAxe] = FFTR(dataDist-mean(dataDist),timeSamp);

% Display
subplot(2,1,1)
plot(xAxis,dataDist,'.-');grid on;axis tight
xlabel('Time');ylabel('Amplitude');
subplot(2,1,2)
plot(fftAxe,fftR,'.-');
xlabel('Frequency');ylabel('Amplitude');
axis tight;;grid on