This is one of the more thoughtful posts in this thread.

You raise some good questions - the right questions to ask - and I don’t have any pat answers to them.
I think it is right to balance the cost to those already in the community with the good that we might do for those who would like to belong. And it is also right to recognize that we cannot help everyone, or even a small fraction of those needing help. And I don’t think we have a obligation to try to do the impossible.
When the Good Samaritan came upon the man beaten on the road, he only helped that one man. There may have been others in need traveling on the road that same day. He didn’t help them, and that’s OK. This one act (fictional though it was) could not be seen as substantially improving the overall conditions of the road to Jericho. Similarly, we need not shrink from helping
some people just because we cannot help** all** people.
As for balancing harms, both internal and external, this needs to be done as objectively as possible, based on a realistic assessment of harms to both the citizens here and the immigrants who might be deported. It is not enough to simply say “I don’t feel safe” without some attempt at justifying that fear with reason. I think some of the views expressed in this thread have tried to make the point that whatever someone feels about their own welfare is sufficient reason to reject the risk of helping those in need.
As for open borders and unrestricted immigration, that is an exaggeration that is not really a position anyone takes seriously. There is nothing contradictory in having a tight border, maybe even with Trump’s big wall, and a reasonable deportation policy, together with a partial amnesty for some (not all) of the illegal immigrants here now. I know people say that an amnesty encourages more attempts at crossing the border illegally, and maybe that’s true. But we should not be relying exclusively on disincentives for trying. For one thing, disincentives can be maintained by who the amnesty applies to. If it is perceived as something for which it is difficult to qualify, the incentive for illegal entry is reduced. Secondly, if we really thought disincentives were the way to go, the border would not be a wall, but a band of land mines followed by a river of swamp adders.
While I cannot answer the very specific questions you ask, I will offer just one guiding thought. We recognize that this entire world was given to us by God - not because we earned it or merit it in any way, but because it pleased God to do so. In particular, the region of the world we now inhabit is part of the undeserved gift - of which we are stewards, not absolute owners. (This is not to deny the concept of private property in human affairs.) It was not too long ago that this land was inhabited by a different people. The land did not belong to them either, even though they were here longer than we Europeans have been here. We don’t create the land - we find it. We improve it, as I’m sure you know better than I do in your ranching. But those improvements are what God expects of us as faithful stewards. It still belongs ultimately to Him. And as stewards, we are charged with presenting God with a return on His investment. Sharing the blessing of God’s gift rather than hoarding it does seem to be something God has encouraged us to do.
How all this informs immigration policy is hard to say, but I think it should at least be kept in mind as we make these decisions.