So you can rather do εσύ έχεις or 'έχεις (with an apostrophe) or am I missing something?
"Εσύ έχεις" means "you have".
However, "εσύ" is the personal pronoun, which can be omitted. In fact, most native speakers (including me) almost never use the personal pronouns when talking. So you can just say "έχεις" (without an apostrophe). :-)
What you call an apostrophe is actually the accent mark. You must have seen it like this: Έχεις in another sentence. When the accent mark is put in the first capital letter of a word, it is always put like this. Ά=ά Έ=έ Ή=ή Ί=ί Ό=ό Ύ=ύ Ώ=ώ
No, it's not. (with the apostrophe) was because he was shortening it