Yes, God made everything that lives on the earth -- including the animals. In the beginning, the Bible says, "God said, 'Let the land produce living creatures according to their kinds: livestock, creatures that move along the ground, and wild animals....' And it was so" (Genesis 1:24).
And yes, the Bible commands us to take care of the animals under our care. One of the signs of a righteous man, the Bible says, is that he takes care of his animals (see Proverbs 12:10). Even the animal of an enemy was to be treated kindly: "If you come across your enemy's ox or donkey wandering off, be sure to take it back to him" (Exodus 23:4). One reason God commanded His people to rest one day out of seven was so their animals would be refreshed (see Exodus 23:12).
In fact, the Bible says we must never treat any part of God's creation with contempt. When we do, we are indirectly treating our Creator with contempt. Instead, God calls us to be stewards or trustees of His creation, and the Bible reminds us that we are responsible to Him for the way we treat it. We've often forgotten this -- but it's still true, and when we ignore it we not only hurt God's creation but we also hurt ourselves.
Most of all, however, God calls us to put Him first in our lives. He loves us, and our greatest calling is to respond to His love by opening our hearts and lives to His Son, Jesus Christ.