Those are low frequencies for a spectrum analyzer. I have used R&S S.A. where the smallest frequecny was 10Hz.
When you mention "power spectrum", are you talking about a power meter or frequency counter to obtain a value for the frequency between 1 to 100 Hz?
As for the number of samples, you don't get any statistical significance below 3. But that does not mean that it should be your minimum value. There are other factors such as when do you need the measurement? For instance, if you must process measurements every 5 seconds and the frequency is 1 Hz, then 3 or 4 would be the maximum number of samples that you could process, unless you have a running average.
Do you have specs for the measurements that you have to take other than the frequency?
JLV