Here John probably means that believers' ability to love God and each other sincerely (See: 1 John 3:18) is a sign that their new life has indeed originated from the truth about Christ.
"we belong to the truth" or AT: "we are living according the way Jesus taught us"
The word "heart" here refers to feelings. AT: "we do not feel guilty" (See: rc://en/ta/man/translate/figs-metonymy)
"Hearts" here is a metonym for "thoughts and intentions." AT: "if the way we think and the way we intend to act make us feel guilty" (See: rc://en/ta/man/translate/figs-metonymy).
God knows more than a person and judges better. The effect of this truth is probably that God is more merciful than our consciences would suppose. This quality of God is expressed by the term "greater." AT: "God knows more than we do" (See: rc://en/ta/man/translate/figs-metonymy)
"You people whom I love" or "Dear friends." See how you translated this in 1 John 2:7.
God's opinion is spoken of as if it depends on what he sees happen in front of himself. AT: "we do what pleases him" (See: rc://en/ta/man/translate/figs-metaphor)