When can I take away a player's scholarship? The window is from the end of the job change period to the cycle just prior signing.
What will the negative effect on my reputation be? If you are cutting a player you did not sign then the penalty is basically non-existant. Everything is factored by decimal points behind the scenes and unless you happen to be a tick above a breakpoint you won't even notice it.
Will I get the recruiting money for the newly-opened slot? If you fill the spot you will not get any additional cash. If you take a walk-on, you will get the cash the following season.