1. Were you self-taught or did you get lessons from a professional? --I had lessons on flute in 5th and 6th grade. My parents didn't have the money to continue to rent the instrument, so I taught myself French Horn, Cornet, Basson, Oboe, Sax, Trombone, and Clarinet...whatever the band had open. Later I went on to major in music in college. Had private lessons in French Horn and Piano, and class lessons in just about everything else.
.
2. How would you rate your skill level? --Decent. 9th grade level on most band instruments, only the bare-bones basics on the strings, and college level on the French Horn. I haven't played in a while though, so it would take me some practice to undo the rust.
.
3. What would you say are the benefits of lessons or self teaching?It all depends on what you're looking to achieve. If you're just looking to play in the local community band, you don't need a teacher...just have fun with it.
If you're looking to play better than just a basic level, then I'd probably get a teacher. Though, be clear and upfront about what you're looking to accomplish. A lot of inexperienced teachers only know how to run you through a book on a weekly basis...something you can do yourself after a trip to the music store for the lesson book. When you talk to the prospective teacher the first time, make it an interview to see if they can meet your needs to fill the position. Most of the major things you would need a teacher for at the beginning are to correct physical habits (from how you hold the horn, embochure issues, breathing issues, tongue placement issues, etc) until you get more skilled. After that their job is more about listening and correcting what you do musically/technically with the music itself, and about pushing your boundaries/skill-level.
.
You played for two years. How serious were you? Did you learn how to form a proper embouchure (and do you remember any of it

)? That's the foundation for how you play...and if the foundation is horrible, the rest will be too. If you have airy tone or sound like a goose, you may want to have a teacher run through embouchure basics with you. (provided the sax doesn't have leaks (which will cause squeaking and possibly an airy tone), you're not using a reed that's too soft (like a #1, which could sound like a sloppy goose) or a reed that's too hard (like a #4, which could get airy...it takes a bit to learn the emboucure control to use the harder reeds.) (I usually started students with a #2, and increased it from there if they could do it without getting airy or tiring quickly.)
If you know what you're looking for, you can find a lot of "do-it-yourself" information on the internet, like here:
http://wiltonelder.com/saxophone-embouchure-five-tips-for-beginners.
How well did you learn musical notation? The beginner lesson books will get you the basics (whole notes, rests, cut-time, etc), but if you want to improvise or learn to play moderate to difficult pieces, you'll want to learn/memorize your scales and arpeggios. Not something a teacher can help with, it's just rote memorization.
.
Hrmm...before I ramble on further, what exactly are your goals? Teachers can be good for many things that I didn't list here, but to get what you want without wasting a ton of money, you'll need to know where you're going. While it may be a "desirable talent to have," how do you want to use that talent? Community band? Jazz Improv? Solos at your church service? Duets with your SO? Just in the privacy of your own home? Street musician? And what skill level do you want to achieve? (ie are there any songs/recordings you've heard where you say "I want to learn to play that!")