J “grew” = auxano. From auksano (to grow or enlarge, whether literal or figurative). This is growing whether in size or mature or greatness or some other metric.
K “became” = ginomai. This is to come into being, to happen, become, be born. It can be to emerge from one state or condition to another or is coming into being with the sense of movement or growth.
L “birds” = peteinon. 14x in NT. From petomai (to fly). This is something with wings i.e. a bird.
M “air” = ouranos. May be related to oros (mountain, hill) with the notion of height. This is the air, the sky, the atmosphere, and heaven. It is the sky that is visible and the spiritual heaven where God dwells. Heaven implies happiness, power, and eternity.
N “made nests” = kataskenoo. 4x in NT. From kata (down, against, throughout, among) + skenoo (to encamp, pitch a tent, dwell); {from skenos (tent, booth, tabernacle, or dwelling)}. It could be a cloth hut. This is a tent in a literal or figurative sense); {perhaps related to skeuos (vessel, tool, container, implement; also vessel in a figurative or literal sense) or perhaps related to skia (shadow, thick darkness, outline; figurative for a spiritual situation that is good or bad)}. This is to encamp or dwell. It is used figuratively for to lodge, stay or rest.
O “branches” = klados. 11x in NT. From klao (to break in pieces as one breaks bread). This is a branch, twig, or bough. It can also refer to descendants.