Okay, I've had this mod installed since the very beginning, so heres my answers to your questions.
1) No, you still see everyone who's online in the same place. it is unaffected.
2) I'm not 100% sure, but I don't think it will, as it will still have to actually open the file, rewrite it, and close it again. which is where the slowness comes from. as I understand it, this mod's stops YaBB writing to the file, thus speeding it up considerably.
3) you could upload a blank file with the same name, and overwrite your existing one. I'd prefer to download the log though, that way there is a backup. but because of the answer to 2, I don't think you'll be doing it anway!
4) No, Deleting the log file won't stop YaBB showing whos online (as far as I know)
Hope it helps