The word translated as assembly is usually translated "church." It refers to God's gathered people.
God's firstborn children are those who are part of the new covenant (see Hebrews 1:6; 2:10–13).
The idea that God's people have their names written in heaven shows God's special care for them (see also Exodus 32:32; Psalm 69:28; Isaiah 4:3; Daniel 12:1; Luke 10:20; Philippians 4:3; Revelation 3:5).
For God's children, God as judge is the one who defends them (see Psalms 9:8; 58:11; 94:2; Isaiah 11:4; Jeremiah 22:16).
Those who have died are now made perfect through Christ's sacrifice (Hebrews 10:14).