Will the people of Paradise work in Paradise, and will there be worship in it?

We do not know what the questioner means by the actions of the people of Paradise. If he means earning a livelihood, they are beyond need of such, and anything of that nature would only be for pleasure and desire, as Allah the Almighty said: {And therein is whatever the souls desire and [what] delights the eyes, and you will abide therein eternally.}

As for worship in Paradise, it is not a realm of obligation, but rather a realm of recompense, honor, and delight. Ibn al-Qayyim mentioned in "Hadi al-Arwah" that acts of worship, except for the remembrance of Allah, will cease in Paradise, as remembrance is perpetual.

Dr. Omar Al-Ashqar mentioned that glorification (Tasbeeh) is not a matter of obligation. Ibn Hajar said: This glorification is not a matter of obligation or imposition, just as breathing entails no burden on a person. So, their breathing is made into glorification.