Learn Spanish (Latin America): Ella es fuerte e independiente.

In Spanish, the word for "and" is usually y. However, when the word right after it starts with an "ee" sound (spelled with an i- or hi-), the y changes to an e to make it easier to say. Since independiente starts with an i, we use e independiente so the sounds don't blend together awkwardly.

Since ella (she) is feminine, shouldn't the adjectives be "fuerta" and "independienta"?

Not all adjectives change their ending to match gender. Adjectives that end in -e in their base form, like fuerte and independiente, are gender-neutral. You use the exact same word whether you are describing a man (él es fuerte) or a woman (ella es fuerte).

Why do we use es instead of está to say she is strong and independent?

We use es (from the verb ser) to describe characteristics that define a person's core identity, traits, or personality. Because being strong and independent are seen as part of who she is as a person, rather than a temporary mood or physical condition, es is the correct choice here.