Is there a supernatural realm or an afterlife?

Answer 1

We don't know. We have no way of knowing through the scientific method. We live in a physical reality governed by the laws of nature. This is what science studies and can only study. Whether there exists a supernatural dimension or what the meaning of human life and the universe is can only be answered by questions outside of science. This is where faith and by extension religion, morality, and philosophy come in. These fields of human knowledge can address and answer such questions, not science whose concentration is solely on the natural world.

Answer 2

Yes, according to the Abrahamic tradition (and others).

One of the central beliefs of Judaism, as stated in the Talmud (Mishna, Sanhedrin 11:1) and codified by Rambam (Maimonides, 1135-1204), is that the soul continues to exist and is treated in accordance with the person's actions while he or she was alive.
The Hebrew Bible doesn't dwell at length on the afterlife; and nor does Judaism spend a lot of time speculating on its details. However, that is not meant to diminish from its importance. Rather, the Torah implies that we are to use the bulk of our energies in keeping God's ways and commands in this world, with our feet firmly planted on Earth, while nonetheless not losing awareness of our beliefs.
Our ancient sages stated the importance of being aware of the next world: "This world is a mere entrance-hall before the afterlife" (Mishna, Avot ch.4).

All outstanding accounts are settled after this life. Some cases illustrate this point, since this entire world wouldn't be enough to reward a Moses or punish a Hitler. And while we're alive, knowledge of the future world serves as one of the motivations to keeping God's will.

The Hebrew Bible does not delve into detail of the rewards of the righteous because the various religions might get into a competition of who promises the most. Also because belief in the afterlife was shared by all ancient societies and needed little reiteration. Besides, it would be like describing the colors of a sunrise to someone who was blind from birth.
It is, however, referred to briefly in Torah verses such as Genesis 15:15, which states that "You (Abraham) will come to your fathers in peace and will be buried in good old age." Coming to his fathers does not mean simply to be buried with them, since Abraham was not buried with his ancestors. Such verses are stated many times.
The prophets are more explicit with such references (see Isaiah 26:19 and 66:24, Daniel 12:13, Zechariah 3:7, 1 Kings 8:30, 2 Kings ch.2, Ecclesiastes 12:7). The afterlife is spoken of at length in the Talmud. More than 20 pages of Talmud (Sanhedrin 90-110, Rosh Hashanah 16-18, and other passages) are given to this subject.

See also:

How do you know there are a heaven and hell?