Yes but in the case of the Catholic Church we have a doctrine called the Gelasian doctrine of the two-swords. Such that for every person who claims to be part of Christendom the authority of the Church is to be set at a higher level than that of any civil authority. And should the later contradict the former, we are to side with the Church. That is part of our faith. It is true that in the broad sense the authority of governments to exercise power comes from God, as must all authority by it's very nature, however in the particular governments can and do negate their authority by acting against God's will and His commands. Otherwise Romans 13 could be used to justify any form of tyranny. Romans 13 only stipulates that in general we are to follow and obey the civil authority's because God has given them power even though they maybe pagan, and as it stands we cannot question God's will. But again, that is in the broad sense, are we to “obey” the civil authority when Christianity is made illegal?
Illegal immigration policy has no bearing to any of the scriptural passages used to support your position. It's not cruel, inhuman, or unjust to ask aliens to abide by the laws of the land they've chosen to invade. The question here is advocating that they be beaten, starved, killed, et c.,. They're just being escorted back to their country of birth. Mexico happens to be the 5th richest nation on earth. Sending them back is not cruel.
Obviously not. One of the points that I was making is that one can find a quote in the bible to justify anything. Also, I do not consider it moral to allow your country to be destroyed by illegal citizens. In this case, Romans 13 has a single edged blade.