Were animals back then dangerous to each others, such as predators stalking and killing their prey? And were they dangerous to people like they so often are today?
According to Genesis there were no carnivores in God’s original creation.
Genesis 1:29 and 30 And God said, Behold, I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, in the which is the fruit of a tree yielding seed; to you it shall be for meat. * And to every beast of the earth, and to every fowl of the air, and to every thing that creepeth upon the earth, wherein there is life, I have given every green herb for meat: and it was so*.
God even told Adam that he would till the Earth in order to eat.
Genesis 3:17 through 19 And unto Adam he said, Because thou hast hearkened unto the voice of thy wife, and hast eaten of the tree, of which I commanded thee, saying, Thou shalt not eat of it: cursed is the ground for thy sake; in sorrow shalt thou eat of it all the days of thy life; Thorns also and thistles shall it bring forth to thee; and thou shalt eat the herb of the field; In the sweat of thy face shalt thou eat bread, till thou return unto the ground; for out of it wast thou taken: for dust thou art, and unto dust shalt thou return.
Since there were no meat eaters there would have been no reason for animals to fear either man or other beasts. God changed things with the birth of Noah.
Genesis 5:28 and 29 And Lamech lived an hundred eighty and two years, and begat a son: And he called his name Noah, saying, This same shall comfort us concerning our work and toil of our hands, because of the ground which the LORD hath cursed.
But God did not cause that prophesy to come to fruition until he had purified the Earth through the Flood.
Genesis 9:1 through3 And God blessed Noah and his sons, and said unto them, Be fruitful, and multiply, and replenish the earth. And the fear of you and the dread of you shall be upon every beast of the earth, and upon every fowl of the air, upon all that moveth upon the earth, and upon all the fishes of the sea; into your hand are they delivered. Every moving thing that liveth shall be meat for you; even as the green herb have I given you all things.
Although it does not say that he gave certain of the animals the same ability to eat meat it must be assumed that that was so.
Hope this helps you to understand the fear of animals for man and other animals.