Second one : I have lots of dreams (me too !!!! ^^ ) or... I have a lot of dreams.

I have "a lots of dreams" is not correct (grammatically). Both of the following would be accurate: I have A LOT of dreams. I have LOTS of dreams. This is similar to saying the following: I have A FRIEND. I have FRIENDS. In both cases, the indefinite article is needed when the term is used in the *singular* form. Source: American English, self

Seems to me that a lot of = many, lots of =plenty...?

Im nut sure wich is right, but you should say a lot of... Or lots of...

Beware of that "a", it indicates one single thing. So "a lots of" is impossible. "I have a lot of dreams" - "a lot" is a group. So you mean many. "I have lots of dreams" - "lots", as in several groups, Again, it means many. "A lot/lots" is slightly colloquial, so better writers would choose something like "many" or "quite a few".