"It is not yours." does not translate as "Není tvůj." You'd have to have the possessive pronoun in neuter "Není tvoje."
Not necessarily. It really depends on the gender of the noun. For example, "syn" (son) and "dům" (house) are both masculine nouns in Czech, and this sentence "Není tvůj" could be applied to both of them, and yet in English they would be translated differently.
ten syn není tvůj - son - he is not yours ten dům není tvůj - house - it is not yours
"Není tvoje" would be used only with nouns in neuter: to dítě není tvoje - the child is not yours to auto není tvoje - the car is not yours