Does the Catholic Church have the authority to make laws and precepts?
Yes, the Church does have the authority to make laws and precepts, an authority granted by Christ Himself.
To Peter, the Church's first pope, Jesus said:
"He who hears you hears me, and he who rejects you rejects me, and he who rejects me rejects him who sent me." (Luke 10:16)
This power was given to the pope in a special way, as is evident by the presentation of the keys. Finally, the bishops, by way of their predecessors, the apostles, were given this power in a lesser way (absent of the "keys") when Jesus said:
"I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earthed shall be loosed in heaven." (Matthew 16:19)
"Truly, I say to you, whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven." (Matthew 18:18)
The reason the Church makes laws and precepts is, "to guarantee to the faithful the very necessary minimum in the spirit of prayer and moral effort, [and] in the growth in love of God and neighbor…" (Catechism of the Catholic Church, 2041)