먹이다 is the causative of 먹다 — making someone else eat or drink — and the "-아/어" form in front says how. 떠 먹이다, spoon-feeding, is the commonest here, and it goes figurative for handing someone information they should have found themselves: you like being spoon-fed, I've spoon-fed you the lot. 타 먹이다 is mixing something into a drink and giving it — you drugged me? The rest cover a grandmother feeding tonic and a soup poured over rice and fed to someone.