Learn Swedish: Vi har inga obligatoriska möten, så du behöver inte stressa. - We have no mandatory meetings, so you do not need to stress.

Behöver inte means you do not have to do something, but you could if you really wanted to (it expresses a lack of necessity). If we used får inte, it would mean you are strictly forbidden from stressing! Since not stressing is a relief rather than a strict rule, behöver inte is the right choice here.

Is it wrong to put att before stressa?

Yes, it would be incorrect here. When behöver is used as a helping verb meaning need to, it takes a bare infinitive. This means the next verb, stressa, goes straight into its basic dictionary form without the word att (to). You just say behöver inte stressa.

Why does the adjective obligatoriska end in -a?

In Swedish, adjectives almost always take an -a at the end when they describe plural nouns. Because the sentence is talking about plural meetings (möten), the adjective obligatorisk (mandatory) has to match it by taking the plural ending -a.

Is möten in the definite or indefinite form here?