Why does water evaporate more in warm air than in cold air?

Because the warm air can hold more of the fine particles of water, and, therefore, can absorb more.

Why does water evaporate more slowly in damp weather than in dry weather?

Because the damp air contains so much moisture that but little more can pass off into it.

What example have we of this?

Wet clothes dry much more slowly when the air is damp than when it is dry.

Why do clothes dry more rapidly in windy weather?

Because the damp air in contact with them is blown away, and the dry air is constantly taking its place.

Is heat necessary in evaporation?

Heat is necessary to produce evaporation.