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It's a irregular waveform.Numerical Integration is necessary but it's pretty difficult to implement in uC .
Another solution is to use external RMS-DC Converter.It will be very practical and the DC value is proportional to RMS value of the waveform.
There is no precise answer to this question; in the end it will depend on the amount of samples per complete cycle of the waveform. Note that signals like the above one, having segments with high skew rate require a higher sampling rate.
Calculate FFT of this signal whatever method (on oscilloscope or on PC) and get fmax of this signal.
Your ADC must samples faster then 2*fmax.
Calculate squares of the samples then calculate mean value and at the end calculate root (LUT as possible implementation of the root function of desired resolution).
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