Which would be what, 'wear a beanie'? I don't know, maaaybe, but I don't think it's good enough to accept it.
"Taking care" of something implies some long term activity, like washing it every day, keeping the hair the right length, and so on. "Mind"/"Watch" in this kind of sentence is more of an avoidance of an immediate threat, like a low beam that you are about to walk into.
no, never. "ę" at the end of the word is often (in real life) or always (by duolingo TTS) pronounced the same way as polish "e"
Hahah :D No, it's only with "uważać". It has multiple meanings, including "to think (to have an opinion)" and "to watch out".
You can only look out for something that is around you, not for something that is already attached to your body. That's the way I see it.
Not quite the same thing. "Look out for your head" more means to look out on behalf of your head; like looking for something which might injure head.
That is somewhat similar to "take care of" which I explained in earlier comment.
I think not. "Mind your head" (common on signs, for example), "Watch your head" or "Watch out for your head".
"Watch out your head", however, is something I think is only said in what is meant to be a stereotypical southern European accent in English language movies, for example in the Marx Brothers - "Watch outta your head". Or perhaps by Manuel in Falty Towers. :)