Were Abu Bakr and Husayn ibn Ali alive at the same time?
Yes. Abu Bakr and Husayn ibn Ali were alive at the same time for 8 years, from AD 626 to AD 634.
Husayn ibn Ali was 8 when Abu Bakr died.
Husayn ibn Ali
Grandson of Muhammad and the 3rd Shia Imam
Born 9 January AD 626 · died 10 October AD 680, aged 54