벌써 is more like a surprised "already" like "It's already 4:00??" whereas 이미 is just a normal "already" like "I already brushed my teeth"

Such subtle difference exists indeed but in reality, even the native speakers speak in both ways. :D

그는 이미 퇴근했어요. = 그는 벌써 퇴근했어요 = He already called it a day. 그는 이미 죽었어요 = 그는 벌써 죽었어요 = He is already dead 그녀는 이미 취했어요 = 그녀는 벌써 취했어요 = She is already drunk

"It's already 4:00??" = 벌써 4시입니까? 4시입니까, 벌써? (sounds natural) 이미 4시 입니까? (okish but sounds a little bit weird, grammatically correct though)

For asking questions, the use of 벌써 rather than 이미 seems safer, I think :D