'Je prends mon chapeau' not correct?
'Je prends mon chapeau' means I take my hat.
In this case it's "I take OFF my hat"
Je retire mon chapeau, is it valid?
Am I obliged to always write "J'enleve" or could I optionally write "Je enleve"?
Writing "j'enlève" is mandatory, "je enlève" is simply wrong.
"Je te(/vous) tire mon chapeau." would be more useful! :-)