So if a Seifert surface of a knot K has positive genus, what can we say about the its complement's first fundamental group, is it Abelian because the only knot with Seifert surface of positive knot is the unknot?
The only knot whose complement has an abelian fundamental group is the unknot. The fundamental group of a knot complement abelianizes to $\mathbb Z$ by Alexander Duality. So in fact the only possible abelian fundamental group for a knot complement is $\mathbb Z$. It is known that the unknot is the only knot where $\pi_1$ of the complement is $\mathbb Z$.