Learn French: C'est une variante qui donne beaucoup de points. - It is a variant that gives a lot of points.

In this sentence, there is no ambiguity about the subject of the relative clause. The pronoun qui immediately follows its only possible antecedent (une variante), and there are no other nouns nearby that could cause confusion. You only step up to using lequel or laquelle as a subject when you specifically need their gender or number to clarify which of multiple preceding nouns is doing the action.

Because variante is feminine, could we say Elle est une variante instead of C'est une variante?

No, you must use C'est here. In French, when you introduce or identify a noun that includes a determiner (like the article une), you almost always use C'est. You use Il est or Elle est when describing someone or something with an unmodified adjective or an unarticulated profession (like Elle est intelligente).

Why is it beaucoup de points and not beaucoup des points?

Expressions of quantity like beaucoup, peu, trop, and assez are almost always followed by just de (or d') without the definite plural article (les). You would only use des (which is de + les) if you were talking about a specific, previously defined group of points, rather than points in general.