Were Abu Nuwas and Ādi Shankara alive at the same time?
Yes. Abu Nuwas and Ādi Shankara were alive at the same time, from c. AD 788 to AD 814.
Ādi Shankara
An Indian philosopher and theologian who consolidated the doctrine of Advaita Vedanta and revitalized Sanskrit scholasticism.
Born c. AD 788 · died AD 817–823