To be alone in the Bible represents being free of evil and false influences. That's why the Lord seeks solitude to pray, and why the nation of Israel is often described as "dwelling alone." When "alone" is used in reference to ownership – when something is "his and his alone" – the meaning is more literal.

In Genesis 2:18, man being alone signifies that the first men became unwilling to be led by the Lord, desiring to lead themselves. In ancient times people who were "Alone" constituted those led by the Lord as celestial men, and evil spirits no longer infested them. But the Jewish church was not meant to be fully under the Lord's guidance and desired to be among the other nations (away from God); and as one who desires is already in evil, this was granted. (Arcana Coelestia 138, 139)

In Genesis 32:24, being alone or by himself signifies good and truth procured. (Arcana Coelestia 4273)

In Exodus 18:14, being alone signifies a state without influx of truth from good from any other source. (Arcana Coelestia 8689)

In Psalm 102:7, alone by itself signifies something of insignificance, and without relative assocation. The state of being alone here symbolizes a prayer of the Lord when in temptations even to despair. (The Inner Meaning of the Prophets and Psalms 352)

In Psalm 136:4, the Lord alone signifies that only the Lord has formed heaven and the church by means of His Divine Truth. (The Inner Meaning of the Prophets and Psalms 386)