Learn Russian: Это дверь. Она не здесь.

Nouns ending in a soft sign (-ь) can be either masculine or feminine, so you generally have to memorize their gender when you learn the word. дверь is feminine, which dictates how the rest of the sentence is built!

Why does the second sentence use Она (she) to mean "it"?

In Russian, all nouns have a grammatical gender, even inanimate objects. When you want to say "it", you must use the pronoun that matches the noun's gender. Because дверь is feminine, "it" becomes она.

If дверь is feminine, why does the first sentence start with the neutral Это instead of the feminine Эта?

When you use это to mean "this is" or "that is" (introducing or pointing something out), it always stays in this default neutral form, regardless of the noun's gender. You would only use the feminine эта if "this" were directly attached to the noun, like in Эта дверь не здесь (This door is not here).

Where is the word for "is" in these sentences?

Russian completely skips the verb "to be" in the present tense. Это дверь literally translates to "This [is] door", and Она не здесь translates to "She [is] not here".