A:
Yes The SA:18250-Telephoto Zoom Lens is supported by your α580
For your convenience here is the complete list of compatible DSLR α series Cameras.
α100, α200, α230, α290, α300, α33, α330, α350, α380, α390, α450, α500, α55, α550, α580, α700, α850, and α900
This lens will also fit the NEX 3, NEX 5 and NEX VG10 with the LA-EA1 mount adapter (Sold Separately)