WOW! I am speechless!!! (Me quedé sin palabras...yeah, I am using 'me' )
I wish I was a better teacher and could explain all your questions in a better way , the one who is really learning here while explaining all of this is me.
Sometimes I don't have the answers and need to read a bit more , understand it in spanish first, and then try to translate it to english.
Now , back to the questions, I think Dan , Rich and Steven have given all the right answers to this matter (I sometimes think they are actually native speakers).
Yes, 'me', "le" , 'te' , etc are all " pronombres reflexivos", the type of pronouns are used to either change the meaning of the verb, put empashis in something or, like in most cases, indicate that the verb or action has a direct effect on the subject.
1)For the first example (change of meaning) we have the following:
¿Ves a ese hombre? Es él que DIRIGE la orquesta. ( Do you see that man? He is the one that directs the orchestra).
Perdone señor, ¿a dónde SE DIRIGE este tren? (Excuse me sir, were is that train headed/going ("directed") to?)
Comí una manzana. (I ate an apple)
Ayer me comí un pollo entero! (Yesterday I ate a whole chicken)!
3) And finally, when the verb has a direct effect on the subject.
El se cortó el pelo (He cut his hair *himself*)
Los 2 gatos se miraban uno al otro (The 2 cats looked at each other*themselves*)
Tu te lo sabes (You know it *yourself*)
Me los encontré (I found them *myself*)
I hope it makes sense!
Me voy, pero regreso pronto (I will go (myself) but I'll be back soon)