Are these absolutely necessary
These and so much more. You have no idea the hassle you are in for.
Yes you can come here with just the passport and apply for a residency card at the immigration office (there is no extended visa or visa at all for US citizens really...just the 90 day entry stamp and the residency card)
Probably the biggest obstacle is you need an official reason to apply...one the Polish government accepts. These are normally Marriage with a Pole...a job or job offer from a company operating in Poland...being a full time student at a Polish university...or a few other rare situations such as being a refugee etc. You can't just get one because you 'want' to stay here. Even if you have one of the above reasons you are in for a whole mess of required documents and things you have never even heard of and will have no end of trouble getting.