what is the actual root verb from this? and what is its meaning? ive seen different translations and im quite confused about it so is this something that depends on context?
« 애가 타 »
« 난 애타는데 »
#“애가 타” meaning
solid harbor
heady hedge
애가 타다 is an idiom that means something like "be anxious/agonized"
애 = fret/worry
타다 = to burn
so basically you're desperately anxious to the point your heart is burning 
there are similar expressions such as
애를 먹다 (먹다 = "to eat") which is like "to be put into a difficult situation"
애를 끓다 (끓다 = "to boil") meaning "to be in a hard time"