is there a way put it to sleep from the IDE?
No, the IDE can only send serial data, it cannot control the running state.
is there a way to clear the serial monitor window?
No, generally I just close it and open it again (though that resets the Arduino too)
Is there a limit to how many lines the window will accommodate?
Don't know the answer to that one.
Is there a way to capture the contents of the serial monitor window in a text file?
Not easily -- you can select all the text as you would select text in a normal window, then paste it into a text editor (Notepad, for example)
You can get more powerful terminal emulator programs (BrayTerm, TeraTerm) which do allow you to clear the screen, log data to a file, etc.
The Flexible MIDI Shield
: MIDI IN/OUT, stacking headers, your choice of I/O pins