Please see the attached file.
There are certain definitions that we need to specify before answering the questions.
Public Good: A public good is a good that is non-rivalrous and non-excludable. Non-rivalry means that consumption of the good by one individual does not reduce availability of the good for consumption by others, or does not preclude consumption by some other user; and non-excludability implies that no one can be effectively excluded from using the good, that is if one person consumes the good then others will do so too.
(a) The first question is whether showing a movie in the dorm-room a public good, and based on the above definition it is. Once you play the movie any number of people can watch it on the video, and say Alfred is watching the movie then it will not reduce Woody's utility from it. That is more than one people can consume the good simultaneously without hurting anyone's utility from the good.
Also, in a dorm room one cannot exclude other boarders from watching the movie, unless you decide to lock someone in a bathroom! One can keep other people out of the room, but not the boarders of the room. Thus, the good is non-excludable ...
A progressive taxation system is summarized.