Learn Swedish: Publiken viftar med flaggan. - The audience waves the flag.

In Swedish, the verb vifta (to wave or flap) requires the preposition med when you are waving an object. Think of it as "the audience is waving with the flag."

Can I use vifta to mean waving hello to someone?

No, and this is a common mix-up! Vifta is only used for the physical action of swinging or flapping something back and forth (like a flag, a dog's tail, or your arms). To wave a greeting to a person, you must use the verb vinka.

Publiken means "the audience", which is a group of people. Is it treated as singular or plural in Swedish?

It is treated as a singular noun (en publik, definite form publiken). While Swedish verbs don't change form based on singular or plural (it is always viftar), this is important to know when adding adjectives, which must take the singular form.

Since it is a whole audience, why is flaggan (the flag) singular instead of plural?

Just like in English, this implies the crowd is either moving one giant flag together, or it is a collective expression. If everyone had their own small flag, you would use the plural definite form instead: publiken viftar med flaggorna.