Learn Swedish: Grannen låtsas att den invasiva växten inte finns överallt. - The neighbor pretends that the invasive plant is not everywhere.

Överallt is a universal spatial adverb meaning "everywhere". In Swedish, adverbs of place typically go at the end of a clause, after the verb and any objects. Even though this is a subordinate clause where the word order changes, the location adverb överallt stays firmly at the end.

Why does inte come before the verb finns here?

Because att den invasiva växten inte finns överallt is a subordinate clause (introduced by att). In Swedish subordinate clauses, sentence adverbs like inte must come before the conjugated verb. This is commonly known as the BIFF rule.

Is låtsas a passive verb here?

No, låtsas (to pretend) is a deponent verb. That means it looks passive because it ends in an -s, but it has an entirely active meaning. It does not drop the -s in any of its active forms.

Could I use är instead of finns to mean that the plant "is" everywhere?

You could grammatically say inte är överallt, but finns is much more natural here. Swedish strongly prefers finns (exists / can be found) rather than är (is) when talking about the physical presence or existence of something in a general location.