I have only ever heard the nickname Jon, Jonty and Jonny used for Jonathan. Based on the way the name is spelled, all of the nicknames you've proposed seem like they'd work perfectly well for Jonathan. You could also shorten the Nathan nickname to Nate.
My only concern is that the name Jonathan is pronounced JOHN-ə-thən in English speaking countries (in German the name is said as: YO-nah-tahn). There is no stress on the last two syllables of the name, and so the 'nathan' part of Jonathan sounds like nə-thən rather than NAY-thən. The same logic is used with the nickname Jonah.