The 1st sentence really looks like consisting of 3 parts.
小白兔回到家里，The white bunny returned home,
种上了菜籽 grew vegetables
兔给白菜浇水 The bunny watered the plants.
给 in itself means to give, but in many cases, just as here, it is used as a "preposition" that marks the benefited person of an action. E.g.
我给你看看。 I show you/I let you have a look. ("I give you a look. ")
我给你带来了一本书。I brought you a book. ("I brought a book to give it to you.")
兔把山羊送的白菜拿回家里。To understand this sentence, you need to take it apart.
山羊送的白菜 means the cabbage that is/was presented by the goat as a present. It is a structure that has 4 parts:
(1) 山羊 the goat
(2) 送 to give (as a present) or to send
(3) 的 attribute particle
(4) 白菜 cabbage
The whole structure is constructed like this: WHO + ACTION + PARTICLE + OBJECT (affected by the action). E.g.
姐姐买的茶 the tea that was bought by elder sister.
拿回 is another thing you need to learn, it is a verb with directional complement, it means take and return (home). A verb is essentially complemented by another verb to show the direction of the movement/action.
There is really no point learning these particles and complements the hard way. Get a grammar reference and work yourself through the examples and the drills. It is a lot easier than trying to translate some easy looking sentence with a dictionary. It is too confusing the way you are trying to do this.
He idled his days away, when he was hungry, he just dined on the cabbage given to him by the goat, and soon the cabbage was all eaten up.
There was a wrong character in the 3rd sentence, I suppose it is 饿 not 饯.