Learn Swedish: Jag hoppas att besvikelsen försvinner. - I hope that the disappointment disappears.

It is derived from the adjective besviken (disappointed). By adding the abstract suffix -else, we create the noun besvikelse (disappointment). Nouns ending in -else are almost always en-words, which is why the definite form here is besvikelsen.

Hoppas ends in an -s. Is it a passive verb here?

No, hoppas is a deponent verb. It has a passive-looking -s ending but an entirely active meaning ("to hope"). As a B2 learner, you have likely encountered other common deponent verbs like minnas (to remember) and andas (to breathe).

Do I always have to use att (that) after hoppas?

Not always. In spoken and informal Swedish, it is incredibly common to drop att after verbs of thinking, feeling, and communicating (like hoppas, tror, and tycker). Saying Jag hoppas besvikelsen försvinner sounds perfectly natural.

What happens to the word order if I want to say "I hope the disappointment does not disappear"?

Because att introduces a subordinate clause (bisats), the negation inte must be placed before the conjugated verb. The sentence would become: Jag hoppas att besvikelsen inte försvinner. This is a great time to recall the "BIFF" rule from earlier levels (In a subordinate clause, 'inte' comes before the finite verb).