Does this strictly refer to physical position or can it be used the same way as english, like to say you're better than someone?
"Sunt mai bun de tine", or "sunt mai bun decat tine" would be "I'm better than you."
"Peste" can be used in lots of ways and contexts, but you wouldn't use it to say you're better than someone.
This can refer to physical position or social hierarchy too, but nobody will say it exactly so.
Also, note that liz's "sunt mai bun de tine" is grammatically wrong (and it sounds very funny for Romanian ears). Correct is "sunt mai bun ca tine" or "sunt mai bun decât tine" for "i am better than you". For ”I am above you”, people will say ”sunt deasupra ta”. That is because ”peste” (see other posts of mine on Duo) is mainly used with moving verbs. ”I pass over you”=”trec peste tine”. ”i sit on you”=”stau pe tine” (think ”kung fu panda”, ”what are you going to do big guy, sit on me?” ”don't tempt me” hehe...) but ”I am above you”=”sunt deasupra ta”.
As it is formulated (with no subject), it can mean "I am" (eu sunt) or "They are" (ei sunt, ele sunt).
Could it be used at "I'm over you" as in a Situation like I don't need someone anymore?
No, it literally means sitting or laying on top of someone.
If you happen to be somewhere above them, swinging in the air or laying above them in a bunk bed, the best word to use is "deasupra" = above.
I'm over you = am trecut peste (I moved on).
"Un pește este peste un pește!" I image Romanians probably have a tongue twisting rhyme about that one?
No. There is no tongue twister here, as we clearly make distinction between ș and s, don't be fooled by their graphic similarity. Think about a tongue twister in English when you say "My mother goes to the market" because g in go is pronounced the same like m in mother and market, and you see how we feel about peste versus pește... :P
Lots of tongue twisters happen when sounds are similar but not the same, though. For example, in English: "She sells seashells by the seashore". It keeps switching back and forth between "s" and "sh" sounds in an irregular pattern. So when people try to say it quickly, they get the wrong one. If it were all the same sound, there would be no tongue twister because there would be nothing to confuse.
Ok, I understand... Like in ”eu pup poala popii, popa pupă poala mea”...