Yes, you can go to law school and get professional job experience at the same time. Almost all ABA accredited law schools in the United States have what are called "Extended Divisions" or "Evening Divisions." These divisions are separated from the regular, full-time divisions and are intended for working professionals who have full-time jobs. Regular division students are restricted (by the ABA) to working only 20 hours a week. Most classes are held in the evening, from 6/6:30is to 10/10:30ish. You complete your degree in three or four years. Some schools require you to complete it in three. Your first semester, the fall semester, you will take 3 classes; the second semester, 3 classes. You can take a summer semester only if your GPA is good. If it is good, it is highly recommended, not only to cut the time but also to lighten the load in the fall, second year because you usually have 4 classes. I can tell you that it is do-able because I am doing it. I work full-time as a paralegal for a law firm and attend Widener University School of Law, Extended Division in Wilmington, Delaware. My commute time is about an hour and 10 minutes, one way. I would recommend 2 things, one you go and get a job working for a law firm or in the legal industry (don't know what your undergrad is in but it doesn't sound like you have legal experience) and work a couple of months BEFORE applying to law school. This way, you get a feel for what you are getting yourself into and you can settle in your new job before adding the stress of law school on top of that.
I understand that eventually you would like to join the FBI and while that is a great and respectable endeavor, you are going to need to keep in the back of your mind that if you don't get into the FBI, more likely than not, you are going to have substantial student loans (unless Mom and Dad are footing the bill) which you will have to begin paying back after you graduate - whether you get into the FBI, or not. Depending on what school you are thinking of going, it's gonna be $100K or more. Therefore, you may have to practice law and there is no sense in doing any of this and incurring the expense, etc., if you are not prepared to have a back-up plan if the FBI has other ideas.
I hope I answered all of your questions but if you have any more, please feel free to e-mail me: lizthompson21061@yahoo.com. Good luck!