This is great for writing in a second language! I don't know how long you have been speaking and writing English, but it's really awesome that you understand it enough to make slant rhyme (lot/top) as well as regular rhyme. 
I will make some edits on English phrases and grammar and I will
italicize the edits, but they are mostly either suggestions or about using periods and commas so do not be discouraged!
Phrasing:You say "Contradiction is part of my last name" and that is a perfect statement, but there is a very similar statement, in American English at least, where people say "middle name" in place of "last name" when talking about something that describes them. So, usually, a person might say
"contradiction is my middle name" in place of "contradiction is part of my last name""but I have only little":
English speakers would more likely say "
but I only have a little" or "
but I have little".
"I want to be an extreme, but I’m right in the middle":
This statement is perfect as it is, but something that might sound better (if you don't mind abandoning the rhyme with "little") is:
I want to be an extreme,
but I'm right in between. Grammar:In most English poetry, the grammar is like any other sentence, except it has line-breaks.
For example:
I want everything, but I have only little. <----
there would be a period at the end of that
thought.I want to be an extreme, but I’m right in the middle. <----
And a period here. I’m moody.
I’m swinging.
I am quite a lot.<----
I, personally, would make each "I'm____" a separate line with periods if each
is a complete thought, but it is not necessary. I’m left, I’m right and I’m right on top.<----
periodContradiction is part of my last name,<-----
comma, because the next line starts with "but".But I’m also pretty much the same.<----
periodI have a body, I have a mind,<----
comma, because the word "Although" is used like the word
"But"Although it’s a slightly different kind.<---
periodThis is a VERY good poem for a second language. I am in school to be an English Teacher, and you have a very good grasp on different techniques already 
I hope to see more posts from you and maybe learn about Dutch poetry!