Learn Russian: Птицы летают в парке.

Летают is a multidirectional verb. We use it here because the birds are flying around in different directions inside the park. If they were flying in one specific direction, we would use the unidirectional verb летят.

Does летают mean they are flying right now, or is it a general habit?

It can mean both! Multidirectional verbs like летать are used for general habits AND for actions happening right now if the movement is aimless or going in many directions at once.

Why is it в парке and not в парк? I thought verbs of motion take the Accusative case.

You are right that destinations take the Accusative case (like в парк meaning to the park). However, the park is not their destination; it is the location where the flying around is taking place. For static locations, we use the Prepositional case (в парке).

How do we know Птицы is plural?

The singular word for bird is птица. Because it is a feminine noun ending in -а, we drop the -а and add -ы to make it plural, giving us птицы.