A question on aliasing and sampling in a measurement system
To answer your questions in order: 


Once the signal is aliased it's like cream in your coffee, you can't really get it back out again. If there was just one strong signal you could notch it out (losing whatever real signal happens to exist at that frequency), but generally once it's mixed in you're scuppered. 
The signals aliasing into different frequencies should not affect the mean if everything behaves linearly and your averaging period does not include an undue amount of aliased very low frequency component. For example, if you had a signal that was being aliased down to 0.01Hz and took a 1 second sample, the mean could be greatly affected. Low frequency components, of course, can be directly affected. 
Ideally the high frequency components (those above the Nyquist frequency) would be negligible. The closer you get to the Nyquist frequency the better your filter has to be. For a high accuracy measurement and a simple single or 2-pole RC frequency you might need to sample at 200 or even 2000x higher than the highest frequency of interest (that's what I came up with in a recent design). 


You would want the passband flatness of your filter to not affect the desired signals. It may be easy to test this with a signal generator. You want the stopband attenuation to be such that negligible signal exists to be aliased down into your signal band. Again you can test this with a signal generator, and compare with actual signal components if you have them available (many oscilloscopes will do a crude FFT- ADC resolution is typically very low on oscilloscopes- that gives you an idea of what is going on). In between the filter rolls off if you have many decades for that to happen it is much easier. You can probably test the DC accuracy much better than you can create an accurate AC signal but if you know the DC accuracy and the passband flatness you can get a pretty good idea of what is going on.