I'm sorry if some of these have already been mentioned, but they aren't on this page at the moment.
You have it as a combination of Typhoon and Explosion.
Since a Typhoon is a watery thing, wouldn't it make more sense for that part of its name to come from one of the following Greek words:
Typhus which means 'hazy' - kind of like the shimmer you can see around something that is extremely hot - just read its pokemon Ruby dex entry for why I think this is the most likely one
>TYPHLOSION obscures itself behind a shimmering heat haze that it creates using its intensely hot flames. This POKéMON creates blazing explosive blasts that burn everything to cinders.
Tefra means ash, or volcanic meterial. Typhlosion is the Volcano pokemon after all.
Thumos means smoke. That is pretty self explanatory.
Ok, the ancient Greek lesson is over. Its just always annoyed me that Typhlosion apparently got its name from Typhoon so I did some digging. Personally, I think the top one is the most likely, but you might completely disagree with all of this anyway, but I just thought I'd mention it.
It seems to me that sylph is a likely root word for its name. A sylph is an air elemental, or a fairy, and Sylveon was the first Fairy type revealed (even if we didn't know it at the time).
Well, the Ink part is fairy obvious, but I have 2 suggestions for the -ay ending.
Spray - as in to spray ink
Okay or M'kay - for this one you kind of need to go to its Japanese name. Bulbapedia suggests its japanese name involves a pun that translates to something like "oh well" or "well, whatever" (Bulbapedia page here) Its name does sound very similar to "M'kay", though. This is purely speculation of course, but it is an idea.
Pikapika is actually japanese onamatapeia (or however you spell it) for 'sparkle', much like chuchu is japanese onamatapeia for 'squeak'. I think this is more likely than coming from the Pika, because Pikachu doesn't look anything like a pika.
I will start this one by saying I agree with both Odd and Radish as root (no pun intended) words. However, I also feel that there is a pun in Oddish's name as well. The -ish suffix is often used to mean "somewhat" or "sort of" so 'Oddish' = 'Sort of Odd' which makes sense considering it's basically a flower pot with legs.
I think this one is just a spelling mistake. It says it comes from artic. Shouldn't it say arctic instead?
It says its name comes from "cross", meaning angry. This is certainly possible, given that its eyes have an angry look to them. However, cross could also refer to the shape it is. With its 4 wings it makes an 'X' or cross shape.
You do say -osis is a common biological suffix. However, it come from either meiosis or mitosis, which are different kinds of cell division, so you could probably specify that.
I read the above suggestion on Pidgeotto/Pidgeot and like the idea, but here is another possible name origin for them. -otto could come from Otto Lilienthal. He was the first person to "make well-documented, repeated, successful, gliding flights" (that's from Wikipedia).
Maybe it comes from jet, which would refer to its very fast speed (Mach 2, according to its pokedex entries).
I mean all of them - Nidoking, Nidorina, etc. The thing about pokemon names is that they are often quite clever, so while Nido may well refer to the pair (as you have on their pages) another possibility is it comes from Cnidocyte (pronounced nee-doh-site). Cnidocytes are a kind of cell found in many poisonous animals, like Jellyfish, Sea Anemones, etc. They are the stinging cells
that are covered in many poison-covered spikes that jab into their target. It seems likely to me that this is another possible origin for Nidoking's (etc.) names.
OK, that's all I can think of for now.