Firstly my schedule as a beta-reader: Don't worry, I am almost always active and can respond on a near daily basis if required - and ONLY if required. The general behavior I take in regards to being a beta reader, is that I am rather fair when it comes handing out criticism, but I will point out flaws when I see them.
Secondly, in regards to the stories or chapters you would hand me, I will also want to talk to you about where your story is headed and might even think you should change bits and pieces of the plot if they don't make sense or are contradictory. If you don't want to, that's fine with me - it's your story after all - but I will strongly recommend it.
I understand that most authors don't like it when something like the plot is touched, but beta-readers do more than check grammar. I feel that so long as the over all core of the story remains untouched, there should be no problem with adjusting the plot.
Also, submit your chapters to me ONLY if I've finished with a previous one, I'm a human not a robot.
Lastly, I will, with all my power, utterly crush character designs the moment I feel it has they are forming a Mary-Sue. At this point I may come off as slightly harsher than usual, but I feel that it is a necessary reaction.
Note: I would enjoy having feedback when beta-reading your story. So if you disagree with my choices, tell me why, I am open to constructive criticism.