That's awesome news! Fingers crossed that they take you on, I'm sure you'd do a fantastic job.
Yeah, they're young and impressionable, so usually musically related stuff grabs their attention straight away if the lesson is practical and involves instruments, even if it is an improvised tambourine, haha. And I think 11-13 year olds will be easy enough to teach. Bearing in mind they're beginners and don't know all the ins and outs of the sax/guitar, they'll probably be impressed by my ability, despite the fact that I only play guitar as a leisure instrument really, aha. I did an A level in maths so I'm secure if that ever comes up :P.
I certainly do! The best books are the ABRSM grades 1-5 Music Theory In Practice books, without a doubt. Here's a link to the grade 1 theory book. The other grades can be found on that website, too. You probably wont need to go into grades 6-8 unless you're really into learning about classical music.
The Beach Boys are incredible. Brian Wilson's vocal style is one that I try to imitate often. That song is pretty sweet too, the bit from 4:09 and 7:34 are my favourite parts. Dat piano.
Jazz piano is fudging awesome. Have you ever heard anything by Vince Guaraldi? He did a lot of the music to accompany the Charlie Brown cartoons. His stuff is incredible. A Charlie Brown Christmas is one of my favourite soundtracks/albums ever.
Here's his absolutely beautiful arrangement of O Tannenbaum. I know it's not Christmas, but it's too good to only listen to during November/December.