As a native Japanese speaker (who played the first two games in Japanese), I feel compelled to point out the following:
"Pika" is from pikapika, the Japanese onomatopoeia for sparkling (like electric sparks). This one was actually confirmed by Tajiri himself. The "chu" part is correct (although specifically, it's the sound a mouse makes).
It is often thought that the "nido" comes from Cnidocyte (which anybody who's taken Bio 2 should know). "Ran" in Japanese can mean "orchard." I also feel the "rhino" thing is a little dubious, as in Japan the word for rhinoceros is sai. But then again, I don't have a better alternative so who knows.
I just want to point out that the "gold" thing may be because psychic stuff in Pokemon is often symbolized with gold, like the Gold Badge (Japanese Marsh Badge).
Almost definitely not "gyre" (Gyarados is his original Japanese name). May be from gyakusatsu (mass slaughter), and dosu (onomatopoeia for puncturing, probably flesh in this case).
While he is based off the Loch Ness monster, the name is probably from either lapis lazuli or Laplace.
Doubtful it's from the cat noise, as "mew" is not an onomatopoeia for cats in Japan. Possibly from mutant.
That's all I got for now.