I just have a few questions about joining the department of homeland security. First, after college, if i want to become a law enforcement officer for DHS, do I apply to them first and then get sent to a academy like FLETC? Next, if there is a DHS base near my home, can i work out of there as my first assignment? Do I have to move homes?

If you want to become a law enforcement officer with the DHS, make sure you meet their qualifications, and apply. If they want you, they will train you. As far as working near your home, that likely depends on what position you get, and where your home is.