I am making a mono-water team, and was thinking of having rain as a weather. Since Politoad is a water type I can set up weather and still keep my mono-type team! This can also be done with the other weathers and Pokemon.
yes, they can. Source: Experience
Yes they can a few examples include an ice type hail team, a rock, ground, or steel sandstorm team (Best I think for this one is rock), a water or grass (while uncommon but I have seen one before) rain team, or a grass or fire type sun team.