Where do animal cells get the molecules, such as proteins, that they use for growth, repair and other life processes?

Animals get protein from diet.

Explanation:

Proteins are one of the important part of diet which constitute about one fifth of an ideal diet. This proteins are formed of amino acids. There are 20 amino acids in nature, of which 9 are essential amino acids and 11 are non essential amino acids. The non essential amino acids are prepared in our body by enzymes. But the essential amino acids are needed to be supplied from outside via diet to get access to. So proteins are needed to be present in diet.

The cells make them from materials the animal takes in from the environment.