Asked to tutor in a class I am currently taking I am in an accelerated Master's program in Engineering, we are taking a Probability course. At this time the class is review for me (I have a B.S. in Mathematics), we are moving very fast though.

One of the other students asked if I would be willing to tutor them, and offered to pay me for the time.

My main worries are that 1. I will get to a point where I am trying to summarize information I have just learned, 2. That I will have a good mathematical explanation but miss the point in plain English, and 3. that tutoring will cause me to not have enough time to study myself.

With those misgivings in mind, would it be more ethical/reasonable to just give some advice for free or to set up payment plan? I am not just going to say "No, I won't help" but if I was charging I would want to be able to give their money's worth.
Like most things in life, being open and honest is a good policy.

Since you (presumably) are not close friends with this individual, and he is asking for assistance it is reasonable to request compensation as a tutor.  Every person on this planet has finite time and resources.  Having a near stranger request time should result in some kind of compensation, mutual friendship, or you should decline.

You can tell him that you're happy to catch him up to where you are while tutoring him, but if the topic advances faster than your learning, either work through the problems with him at a reduced rate (or free if you feel like it's equal contribution) or simply suggest finding another tutor at that point.