Were Jabir ibn Hayyan and Muḥammad ibn Musa al-Khwarizmi alive at the same time?
Yes. Jabir ibn Hayyan and Muḥammad ibn Musa al-Khwarizmi were alive at the same time, from c. AD 780 to AD 815.
Muḥammad ibn Musa al-Khwarizmi
9th-century Persian mathematician and astronomer
Born c. AD 780 · died c. AD 850