Central and Peripheral roles
I'd like to know if with the nRF51 and/or nRF52, we can use our module as Master and Slave at the same time (simultaneously) ?
Yes, the s13x series softdevices (bluetooth stacks) support concurrent GAP central and peripheral roles (master/slave).
The radio can't listen and transmit at the same time. Connection events for Central and peripheral links are handled by the internal scheduler in the softdevice.