Wouldn't experience make it more difficult to get an REU? Since I thought REUs are supposed to be prioritized towards students at lower-tier schools without the resources to perform research at their school so they have a chance to get some experience elsewhere like at an REU
As long as the time requirement for the project doesn't require a sacrifice of attention to your coursework then I see no issue. In my opinion, developing good study habits and a strong foundation of knowledge in your first and second year should take priority, though.
Totally dependent upon institution/individual. Guy I'm working with is extremely flexible.
It depends on the set up too, there is a possibility I'll be getting credit/stipend next semester for research so under those circumstances he'll probably be less lenient.