The document does not provide you with the right to work. Mind, to work illegally is a bad idea. The laws of Cyprus concerning work are strict, and if they catch you even for completely harmless training or yoga, you will face deportation and a fine. It's better not to risk.
With a pink slip, one may leave the island for less than three months, and if one violates this rule, they will cancel the permit automatically.
A pink slip is not available to EU citizens.
They grant a pink slip for one year and can extend it.