READ the ENTIRE play. I cannot stress this enough. Read the whole play, understand your character in the context of the entire play.
Some schools will quiz you on it. Be prepared.

Profanity & Edginess. Don't go so edgy that you make the auditiors uncomfortable. I've heard stories. If the auditor feels the need to look away, you aren't getting in. Now is not the time for edgy, that comes later!
Profanity is generally ok, if it's not excessive and poorly done. If you're comfortable with it, the monologue speaks to you, and you can nail it, go for it.
Do check with each school however, as some state no profanity.

You CAN edit monologues for time. Try to keep your monologue around 1 minute. Common Prescreen is 60-90 seconds with slate, but then the auditions call for a 1-min monologue. Make it easier on yourself now.
Chop off and out lines for time. Just make sure it still makes sense.
We did one where there was dialogue from other characters, just remove those lines, and any lines from your character that no longer make sense with the other dialogue removed.

Prescreen Filming: 3 & Done Rule! First one is a warm up. Second one --you'll nail it. Third one, good measure. Fourth? You lose your spark.
It's noticable. These schools are NOT looking for perfection --listen to the podcasts. They all say it.
They are looking for that spark, your unique artistry. You will drive yourself mad trying to film perfection.
We saw flaws in my son's, we submitted one of the three anyway. He had a 95% prescreen passrate, to include "top tier" schools.
They were still great with the "flaws", and gave him something to focus on in auditions so schools could see an improvement from the prescreens.