Yes, you can do this:
i) there is a useful page on Exp League that gives some things to think about when considering A/B testing in an SEO context.
ii) yes, typically you would take one content section/category page etc and then look for average rankings, with the idea of getting two samples that have similar distributions of rankings that could be A/B tested
iii) yes, this Google article here is pretty useful in terms of understanding potential impact/effects
