I think you can see the back of one in the shuttlebay in TMP (maybe only in the Director's Cut).
Nope, the matte paintings portraying shuttles like this (but not
these - Andrew Probert specifically designed a separate, smaller variant to be seen in the mattes) were left out from all of the incarnations of this movie.
Incidentally, the picture in Mr Scott's Guide
is actually of this smaller variant designed to be seen aboard Kirk's ship; it has the prominent side door and the larger docking tube in relation to overall size.
I'm pretty sure it's the same shuttle that rescues the crew in San Fransisco bay after they let the whales go at the end of Star Trek IV.
Nope, nothing similar about them. The ST4 shuttle has a big, rounded window in front and in general is very rounded overall.
And I think there's one flitting around inside the Spacedock in Star Trek III.
Several - but of the type also seen in ST4, not of the type seen in ST:TMP. The Vulcan shuttle never appears in Star Trek outside ST:TMP.