To remain in someone means to continue to have fellowship with him. See how you translated "remains in God" in [1 John 2:6](../02/06.md). Alternate translation: "we continue to have fellowship with God and he continues to have fellowship with us" or "we stay joined to God and he stays joined to us" (See: [[rc://en/ta/man/translate/figs-metaphor]])
The word "remains" is understood from the previous phrase. Alternate translation: "and he remains in us" (See: [[rc://en/ta/man/translate/figs-ellipsis]])
Your translation may be clearer if you omit either "by this" or "because." Alternate translation: "We know ... us because he gave" or "By this we know ... us: he gave"
"because he gave us his Spirit" or "because he has put his Holy Spirit in us." This phrase, however, does not imply that God has less of his Spirit after he has given us some.