Disclaimer - not a native speaker.
After looking around through dictionaries, this is my opinion.
"Everything" means exactly that, and translates better as "alles". "Jedes" translates to "every" only in the sence of "every thing". As in "Every dog has its day" or "Every other book is damaged." Maybe a native speaker can better enlighten us, but I don't think "jedes" can translate as "everything". Hope that helps!
"Everyone" = people. As in "Everyone is happy about this sentence."
"Jedes" doesn't seem to be used for people (as near as I can tell...not a native speaker), but for items. Possibly "Not every one" will work, as "every one" means things...as in "All of these plates are dirty. Every one of them."
That's just my take on it though. Hope it helps!