Truth and love
The letter never makes them rivals: love is in truth, and truth-shaped obedience takes the form of loving one another.
Walking and abiding
Faithfulness is continuing conduct and remaining, while deceptive 'progress' leaves the teaching behind.
The embodied Christ
The decisive denial concerns Jesus as Christ coming in flesh, and relationship with the Father cannot bypass the Son.
Support means participation
Reception and greeting are morally charged when they provide recognition or practical help to the work.
Family language
Lady, children, and sister can fit a church metaphor, an actual family, or a layered household-community setting; certainty exceeds the evidence.