As for the explanation of how the organic webshooters work and why he'd have spinnerets from his writs...I'm sure that JMS or Joe Q used the logic of oh this is where Peter had his mechanical web shooters so let's make his organic shooters in that place as well and hope not too many fans discuss anatomically correct issues.
Credit where credit is due: the storyline that introduced the organic webshooters was written by Paul Jenkins, in his run on
The Spectacular Spider-Man (collected in TPB form as
Disassembled, because it was a loose tie-in to the
Avengers: Disassembled event, and because in a way it involved Peter being taken apart and put back together in a new form, cocooned by some insect-queen monster and emerging "reborn" with new powers). Jenkins' run on
Peter Parker and
Spectacular tends to get overlooked in the shadow of JMS's
Amazing run, which is a shame, because Jenkins did good work (although
Disassembled was probably the worst storyline of his entire run on Spidey).
JMS never even acknowledged the events of
Disassembled; indeed, the following year, he, Peter David, and Reginald Hudlin collaborated on
The Other: Evolve or Die, in which Peter "died," formed a cocoon, and emerged with new powers -- and not one character even mentioned that something almost identical had just happened a short time before. The powers JMS gave Spidey were "stinger" spikes coming out of his wrists (again the fixation with the wrists) and an enhanced spider-sense that was based on an amplification of real spider senses (totally ignoring the "talk to insects" sense that Jenkins had abortively given him).