I learned that Australian people say "vege/veg out" as slang to mean "do nothing and realax". Do other native speakers (such as American or British people) use it, too?
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
Americans use it too. I wouldn't spell it vege, as my readers would read that unfamiliar word and think "veej".
I am not a teacher.
The -e is unnecessary- we use fruit and veg and pronounce it with a soft g, and the same is true of the verb.
That is an incorrect spelling.