Learn Russian: Мощность нового двигателя превышает норму: она в два раза выше. - The capacity of the new engine exceeds the norm: it is twice as high.

This is the standard way to say "X times more [adjective]" in Russian. You use the preposition в + the accusative number (два) + the word for "time" (раз) + the comparative adjective (выше). Because the number is 2, раз takes the genitive singular form раза. If it were 5 times higher, it would be в пять раз выше using the genitive plural.

Why is the pronoun она used to mean "it" in the second half of the sentence?

Она refers back to the subject of the first clause, мощность (capacity/power). Since мощность is a feminine noun (as are almost all abstract nouns ending in -сть), it must be replaced by the feminine pronoun она, even though it translates to the gender-neutral "it" in English.

What case does the verb превышать take, and why do we see норму here?

The verb превышать (to exceed) takes a direct object in the accusative case, exactly like its English equivalent. Therefore, the feminine noun норма (norm/standard) changes its ending to -у to become the accusative норму.

Could I use the word мощность to talk about a person's physical strength?