How Is Torah Studied in the World to Come?

"Hello. I have some important questions that I asked my parents, but they couldn't answer and suggested I ask you. Here are the questions:
1. Is the Torah in this world the same as that in the world to come?
2. We perform mitzvot in this world to earn the reward of entering the world to come. Will we perform mitzvot there as well? Is there a third world we are anticipating? Thank you."

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Hello and blessings,

The Torah includes peshat (simple interpretation), remez (hints), derash (interpretation), and sod (secret). It is layered such that each verse and mitzvah conceals more profound roots connected to higher worlds.

In the world to come, the deeper layer of Torah, hidden behind verses and mitzvahs, is revealed, as the entire Torah expresses the divine will through human words and situations. For example, mitzvot like loving your neighbor as yourself relate to the root of giving and kindness, studying the laws of sacrifices concerns self-sacrifice and the sanctification of Hashem's name, etc. Every mitzvah has a higher root revealing divine will, thereby bringing the soul closer to its Creator.

In the world to come, the righteous study all parts of the Torah and discover its highest layers, which provide indescribable pleasure to the soul by bringing it closer to its Creator—Hashem, the true source of happiness.

Please watch Rabbi Zamir Cohen's lecture - "The World to Come According to Kabbalah".

The deceased is called "departed" because they are exempt from mitzvot. In the world to come, mitzvot are not performed. Instead, one connects to the source of the mitzvot, which is Hashem. The sages said that in the world to come, the righteous stand with crowns on their heads and enjoy the radiance of the Shechinah. We cannot comprehend the spiritual pleasure of the world to come, which surpasses all possible enjoyments. Torah study in the world to come is on another level, revealing the roots of the mitzvot—that is, the divine will behind them, through which souls connect to their true origin.

However, with the coming of redemption, there will be the resurrection of the dead, and this will be a long period during which the dead will return in body and fulfill mitzvot in the Third Temple in this world. See here a lecture on the end of days.

See here a lecture on Gan Eden and the world to come according to Kabbalah.