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True enough. But if you must touch a stick with shit on it (and hey, shit happens, so it's not an impossibility), I would say the non-shitty end would be the right end and vice versa.
I agree except on the 'head in the clouds' part. To me it seems this is more about being lost in thought (which may be perfectly sound and reasonable thoughts), and thus being unaware of what going on around you.
"Head in the sand" is more about intentionally ignoring something because it's uncomfortable to acknowledge; the equivalent of putting your fingers in your ears and shouting LALALALA when someone is saying something you don't want to hear. Whereas "Head in the clouds" refers to someone who daydreams or gets caught up in their thoughts to the point of becoming unaware of their surroundings. "Head in the game" seems more closely related to the phrase in the OP...if your head is in the game, you are thinking about the task at hand.
You may be right, my opinion is that the phrase could be taken either way without further context. Regardless, the question was about the term "head in wrong place" which has nothing to do with whether the relationship advice is being directed at the older or younger person.
'The' is not being dropped, it is being used in the proper part of the sentence. Where are your references to actual grammatical rules, such as those I included in my answer?
So, just to clarify, if you were swimming at the northern shore of the Red Sea, you would be swimming in the northern Red Sea, not the northern The Red Sea. 'The' may be used as part of a name, but it is still a definitive article, and is treated the same as a definitive article anywhere else. You wouldn't say 'the northern The Thames' or 'the British The Times' or 'the English The Queen' or 'the new The Doon School campus'.