There are better commentaries available on Rom 8:15-16 and Gal 4:6 but these might offer a good starting point:
1. Rom 8:15-16: "For you did not receive the spirit of slavery to fall back into fear, but you have received the Spirit of adoption as sons, by whom we cry, 'Abba! Father!' The Spirit himself bears witness with our spirit that we are children of God."
a. Here's Craig Keener on Rom 8:15-16 from The IVP Bible Background Commentary: New Testament:
"Roman adoption—which could take place at any age—canceled all previous debts and relationships, defining the new son wholly in terms of his new relationship to his father, whose heir he thus became. . . . As a legal act, Roman adoption (cf. 8:15) had to be attested by witnesses; the Spirit is here the attesting witness that God adopts believers in Jesus as his own children."
b. Here's Douglas Moo on Rom 8:14-17 from The New Bible Commentary:
"The Spirit of adoption. As ‘life’ is the ruling idea in vs 1–13, so is sonship in vs 14–17. This brief paragraph, in addition to making its own contribution to the theme of the chapter by recounting the wonderful and comforting truth that Christians have been adopted into God’s own family, provides a transition between vs 1–13 and 18–30. Being a child of God explains both why God’s Spirit confers life on us (13–14) and why it can be said that we are heirs with a glorious prospect for the future (17–18).
"To be led by the Spirit of God (14) means not to be guided by the Spirit in decision-making, but to be under the dominating influence of the Spirit (Gal. 5:18). The clause sums up the various descriptions of life in the Spirit in vs 5–9. Paul can claim that those so led by the Spirit are sons of God and so destined for life (13) because sons of God is a biblical title for the people of God (see, e.g. Dt. 14:1; Is. 43:6; cf. Rom. 9:26). But we must also recognize in the title an allusion to the sonship of Jesus himself (see vs 3 and 29); as v 15 confirms, ‘Abba’ was Jesus’ own address to God (see Mk. 14:36), one that showed especial intimacy. This same address is now one that Christians spontaneously ‘cry out’ in their own approach to God. It is the Spirit, again, who implants in us that sense of intimacy (16) and abolishes, thereby, all bondage (to ‘the law of sin and death’, v 2) and all reason to fear (15a). The Spirit, thus, is the Spirit of sonship. Paul takes the word ‘sonship’ (which could also be translated ‘adoption’—hyiothesia) from the Greco-Roman world, where it denoted the legal institution whereby one could adopt a child and confer on that child all the rights and privileges that would accrue to a natural child. But the conception is rooted in the biblical picture of God as one who graciously chooses a people to be his very own (see 8:23; 9:4; Gal. 4:5; Eph. 1:5)."
2. Here's Gal 4:6: "And because you are sons, God has sent the Spirit of his Son into our hearts, crying, 'Abba! Father!'"
a. Here's Craig Keener on Gal 4:6 from The IVP Bible Background Commentary: New Testament: "Roman adoptions required a witness of the transaction: the Holy Spirit performs this function here. That the Spirit should testify is natural, because Judaism understood the Spirit especially as the one who inspired the prophets; the Spirit here inspires believers, speaking to them as he did to the prophets, to remind them of their calling as God’s children. 'Abba' is the Aramaic word for 'Papa,' a term of special intimacy rarely if ever used in Judaism to address God directly (see comment on Mk 14:36; Rom 8:15)."
b. Here's Moises Silva on Gal 4:6 from The New Bible Commentary: "At this point the apostle reintroduces the theme of the Spirit, with which he had initially appealed to the Galatians (3:3; cf. also 3:14 and possibly the reference to baptism in 3:27). Only now the significance of the Spirit is tied directly to the doctrine of sonship. Since we have received the Spirit of God’s Son, our hearts are conscious that God is our Father and that we are full heirs. Note carefully the expansion of these ideas in Rom. 8:14–17, 26–27."