Hashem wanted Adam and Chava to eat the fruit, but He wanted them to volunteer. He therefore set things up that they should figure it out and do so. The reason is because it is better to be a Baal Teshuva than a Tzaddik, and as a result we would be able to not only reach a higher potential ourselves, but also have the opportunity to bring Hashem Himself in His full Essence into the world, completing the ultimate purpose of creation which is Dira Betachtonim.

You can find a source for your first paragraph here. As for Gan Eden before the sin, please ask that as a separate question.

Sources: Basi Legani 1972, Midrash Tanchuma Vayeshev 4 (thanks @shmosel!!), Rabbi Manis Friedman Shlita.

Hashem wanted Adam and Chava to eat the fruit, but He wanted them to volunteer. He therefore set things up that they should figure it out and do so. The reason is because it is better to be a Baal Teshuva than a Tzaddik, and as a result we would be able to not only reach a higher potential ourselves, but also have the opportunity to bring Hashem Himself in His full Essence into the world, completing the ultimate purpose of creation which is Dira Betachtonim.

You can find a source for your first paragraph here. As for Gan Eden before the sin, please ask that as a separate question.

Sources: Basi Legani 1972, Midrash Tanchuma Vayeshev 4 (thanks @shmosel!!), Rabbi Manis Friedman Shlita.