Learn Italian: La sfortuna esiste, ma io non ci bado. - Bad luck exists, but I do not pay attention to it.

In this sentence, ci doesn't mean "there". It replaces the phrase "to it" (meaning "to bad luck"). The verb badare (to pay attention / to mind) is followed by the preposition a (to). Instead of saying non bado alla sfortuna (I don't pay attention to bad luck), we use ci to replace a + the thing we are talking about.

Is badare a common verb and does it always use a?

badare means "to pay attention", "to mind", or "to look after". It is almost always followed by the preposition a (like badare ai bambini - to look after the kids). Because it requires a, you will see it paired with ci very often when the object has already been mentioned, as in non ci bado (I don't pay attention to it).

Why is the word order non ci bado instead of ci non bado?

Pronouns like ci stick directly to the verb they belong to. The negative word non must go right before the pronoun-verb combo. The strict order is always non + pronoun + conjugated verb.

Why does it say La sfortuna instead of just Sfortuna esiste?