First off, welcome to GC.
Now, to answer some of your questions. It is going to be hard for any of us to answer your informal recruitment question unless one of us is from ASU. Every university (and chapter!) does things a little differently, so I suggest you contact your Office of Greek Affairs. I did some quick searching and come up with this page. I would start here.
ASU Greek Affairs Contact Info They should be able to tell you if/when informal recruitment occurs and which chapter(s) are participating.
Also, it's ok to have boyfriends and be a part of greek life. I had a steady bf throughout my undergrad experience. Really it's up to the individual to balance her sorority and her bf. No problems should arise as long as one stays active and participates in important events.
Good luck,
Erin
Co-Moderator