No, it's derived from fora, meaning "trip" and/or the wares brought on a trip. That word is Old Swedish (and not in use any longer), so it precedes Henry by at least half a millenium, as does fordon. :)
Our word for "car" - bil - is derived from the French automobile, by the way. We took the last part of the word, and the Germans took "Auto".
The loan is well over a century old, and the word is indeed French. See e.g. http://etymonline.com/index.php?term=automobile for a source. I'm aware that it's not a common word in French, but I didn't claim that it was either. I also didn't say automobile in French means "car" specifically.
No, but I'm glad you asked! I'm very fond of its etymology. Considering its history, modern English has very few loans from Celtic languages.
During Julius Caesar's conquest of Gaul, he encountered two-wheeled war chariots of a kind the Romans didn't have. They adopted the technology - and the native word for it: karros. This word still exists in other variations in related languages, such as the Welsh carr meaning "wagon".
Caesar wrote about the carrum in his writings on his military campaign, and from there it has survived through the millenia, and through several other languages on its way to the modern English meaning. :)
We actually have kaross in Swedish as well, which we got from French at some point. It can mean either a really fancy horsedrawn carriage (very rare) or the metal chassis of a motor vehicle (common).
I was totally stumped on this one so I tried different spellings of what I thought I heard in Google translate. My last attempt was fodonat. (I couldn't hear the r) It asked if I meant fodona. I learned a new work in Swedish I certainly won't be using in polite society. :-)