What is the function of अपने in the sentence? I mean, why अपने and not आप or तुम?
In Hindi, पीछे देखो can mean both "Look back" and "Look behind (something/someone)". अपने (meaning: of oneself) is used to specifically imply the first meaning.
A: पीछे देखो। (Look back/behind of...)
B: किसके? (Of what?)
A: अपने! (Of yourself!)
The ambiguity above disappears if A says "अपने पीछे देखो।" in the first place.
The example was just to show the function of अपने. In normal conversations "पीछे देखो" is just as commonly used to mean "Look back" as "अपने पीछे देखो" because context often eliminates the need of अपने.
Is this "apne" the same apne we met before, for example in "वे अपने नाना के साथ रहते हैं" (they live with THEIR OWN grandfather)? that means that if I want to say "I look behind myself" I must use "apnaa" instead of the plural form "apne", for example "मैं अपना पीछे देखता हूँ"? Pls, tons of lingots if you answer
Yes it is the same ownership related word. You must still use the oblique form:अपने - मैं अपने पीछे देखता हूँ... Though sometimes in conversations, the अपने may be omitted when it is obvious from the context