The short answer is that believing on God is the same as believing on Jesus, as they are one. The OT believers looked forward to the Christ's work on the cross, having been given archetypes of the atonement in sacrificial practices and later, The Law. Immediately after Adam and Eve sinned, there was a shedding of blood to provide a covering. Abel's offering, which involved the shedding of blood, was accepted while Cain's, the product of his labor, was rejected. So from the very beginning God provided a revelation pointing to the atonement.
The prophets also spoke of Jesus and what He would do, sometimes cryptically, sometimes symbolically, sometimes in straightforward terms. With the knowledge of the Law and the prophets, the Jewish leaders of the day should have recognized Jesus; at least should have understood what the cross was all about.
The Old Testament believers' faith and practice were according to the revelation they had, but they were only sufficient because Christ was the substance and ultimately object of their faith and practice. They were justified not by the blood of rams and bulls, but by the blood of Jesus.
As for your last question, I'll leave that to others who have studied it more. There are all kinds of discussions about hades and sheol and soul sleep and Abraham's bosom and heaven that tend to make my eyes glaze over.
