To your first point, regardless of which class of people you consider for UBI inclusion, even if you only consider citizens of the USA, it will have a tremendously attractive effect for billions of people around the globe. Even now quite many people want to immigrate in to the USA and the USA has multiple systems designed to keep them out, but UBI will make this
way worse, which is why I said that enforcement needs to be very strict.
Plus I'd say it would be even more unfair for the undocumented immigrants than it is now because they would not get any UBI. But if you gave UBI to the undocumented, way more people would attempt to become undocumented immigrants, by overstaying their visas, etc. Which then probably will lead to you having to issue less short term visas, or actually deporting undocumented immigrants.