The answers to your questions are highly variable among the teachers.
Almost all of the professors that I've had will excuse an absence on the test if you file the illness form while some also require that you notify them by email before the start of the exam. The remedy is usually either to pro-rate the rest of the exams and the final, to give a makeup, or to give you a choice of the two(very rare). Check your syllabus, many profs clearly state their policies there.
Essentially, the short-term illness policy AFAIK
doesn't really specify how professors deal with the absence except that the student shouldn't be penalized. The rest is up to the prof. Of course, your use of the form can be subject to scrutiny by the prof or the dean should you be suspected of abusing it but other than that, I don't think it's possible to be "marked down" for its use.
As for when to submit it, use common sense. It should be the point at which you definitively know you won't be able to take the test. The earlier the better (as a courtesy to the prof) while accounting for the possibility of you recovering in time. It goes without saying that that point should always be before the actual start of the test.