Is Every Finite Complex Representation of a Compact Lie Group Unitary?

[Andre' Quanta]

I am studying Group Theory at the moment and i am not sure about a theorem.
Is it true that a Lie Group G is compact if and only if every finite complex representation of it is unitary?
I know that is true the if, but what about the viceversa?
Same question.
Is it true that a Lie group is compact if and only if every irreducible representaion unitary is finite?

 

[Andre' Quanta]

If a Lie group is not compact is it true that all its irreducibile unitary representations are infinite dimensional?