How can a student stop/report conversations with a professor that make her uncomfortable, while avoiding negative consequences for the student? I have some concerns about the behavior of a professor whose class I am taking, Professor A.

First, Professor A has been trying to involve me in his attempts to get another professor in the department, Professor B, fired:

I am taking different classes from two different professors that are in one department. Professor A has asked me to BCC him on all my emails to Professor B, in case Professor B does not pass me in his class.  I took a class in the Spring semester with Professor B and never had a problem with him. Professor A said he can defend me, to the dean but needs documentation to prove I asked for help during the semester. 

Today, Professor A asked me to write a detailed outline to him about Professor B and all of the things he has not done correctly in my class and then sign it and include my name, the company I work for and my job title. He wants to turn it in to the department chair to have Professor B fired. Professor A continues  the conversation and tells me Professor B was supposed to have been placed on a performance improvement plan, but the school has gone through 4 chancellors so Professor B did not receive any disciplinary action. 

I am also uncomfortable with other conversations I have had with Professor A:

Another time, Professor A asked me to look at an invitation his wife created for a fall fundraiser for the school. Both he and his wife want my opinion. I work in corporate America, but never did fundraising. He asked for my cell phone number to give it to his wife. I didn't think anything of it and gave it to him. He texted me in the classroom so I would have his number. I thought it was very strange. I have stalled the meeting because I am busy with school and work. Plus it seems weird to me. 

Professor A gave me his business card that his wife made him in case I want to contact him outside of school. Apparently, he is a musician when not teaching during the week. 

I am really uncomfortable with these conversations. He waits until after class to have them. He told me he records all conversations on his phone when he speaks with the administration to use it against them in case the administration tries to get rid of him. I think it is unprofessional and unethical to say any of this to a student. 

The semester is half over with and I only want to pass the class and never speak to Professor A again. I have not committed to anything because he creeps me out! I feel like he should be reported to someone, but I don't want anything negative coming back to me. Can someone please help me with what I should do?
This sounds like an instance of mental health problems on the part of the Professor A...

Probably it is simplest to behave "incomprehendingly", to just be unresponsive, disengaged, listless, and generally not react at all to the machinations of the person.

It is unfortunate, but does happen, than people (apart from gender issues) get caught up as "dupes" or "accomplices" in the schemes of mentally ill people who've managed (despite their problems) to get into situations where they have considerable power over others.

While in principle one can file grievances and/or hire lawyers (e.g., in the U.S.), this is often a path that has great costs, psychological, personal time, and one's reputation (even if one "wins").

So, as often is the case, again, if it is feasible, "playing dumb", being unreactive, and just letting the drama pass you by, is probably the most desirable/happiest approach.

(No, "justice" is not served ideally-well by this approach, but it may be served as well as can be...)