Non-compact group, finite dimensional representation, and unitary representation

Are the following statements true about non-compact (Lie) group?

  1. Non-compact group, for every finite dimensional representation $Rightarrow$ must be nonunitary representation

(naively, $p Rightarrow q$)

  1. Non-compact group, for every unitary representation $Rightarrow$ must be infinite dimensional representation

(naively, $sim q Rightarrow sim p$)

  1. Non-compact group, for every nonunitary representation $Rightarrow$ must be finite dimensional representation

(naively, $q Rightarrow p$)

  1. Non-compact group, for every finite dimensional representation $Rightarrow$ must be nonunitary representation

(naively, $sim p Rightarrow sim q$)