There are quite a few female MPs... you become Airborne by either getting it in your contract or excelling in PT and being selected while in your unit for the school.
I was an MP in the Army and I did law enforcement while in the US (stationed @ Fort Stewart, GA) as well as weapons ranges and spending weeks in the field while training for deployment.
In Iraq I worked everything from helping run EPW compounds, to personal security for high ranking people, to combat patrols. I was a .50cal machine gunner and was hand selected for several missions.
As far as being treated the same as males... that is up to you. If you dont complain, dont sleep around, do what youre told, and pull your weight then you will be treated just fine.
If you are offended by cursing or sexual jokes then its probably not for you.
Dont expect to have birthdays, holidays, or weekends off.. because as an MP you will work through those.
As with any job in the military... its only what you make of it. There are some people who complain, but those are usually the ones who stay in trouble. I loved my time in and wish I could go back, but that is not possible. My husband is still in and is currently deployed to Iraq again.