Learn Farsi: لباسِ من خشک نیست.

No, you cannot freely attach nâ- or bi- to any adjective. Just like in English (where we say "wet" instead of "undry"), khoshk doesn't take these prefixes. To express the opposite, you either negate the verb with nist (as done here) or use a completely different vocabulary word like khis (wet).

Is the negative verb nist related to the negative prefix nâ- from this lesson?

They are related concepts but function differently. The word nist is a verb meaning "is not" (historically a contraction of the verbal negative na- and ast). The prefix nâ- from this lesson is used to build permanent negative adjectives (like nâ-dorost for "incorrect"). You use nist to state that something isn't currently a certain way, rather than creating a brand new adjective.

The English translation says "clothes are", which is plural, but nist means "is not". Why is the singular verb used?

In Farsi, the word lebâs can refer to a single garment (a dress, a shirt) or be used as a collective noun for "clothing." Because it is written here in its singular form without a plural suffix like -hâ, it takes the singular verb nist. Literally, it reads "My clothing is not dry."

Could I attach a possessive ending to lebâs instead of using the separate word ?