Yes, you may only get enough to live awesome in "the middle of nowhere" or whatever. So what? If you want to live in San Fran, find a way to get the money to live there.
No it won't, no more than today.
>With basic income you no longer have to live where the jobs are and can move around freely.
Poor people are already "free" to not live in places they can't afford, and instead live in places with poor access to education and healthcare and jobs, and as such have reduced life expectancy. Your plan to use UBI to re-locate and segregate poor is no improvement compared to the current situation.
What may be less obvious is that I also support universal education and in Canada we also generally have that, at least as far as K-12 goes. If I were a parent, my children would have access to the same quality of public education in a small rural town as they would in a rich area of Toronto.
Is this true in reality or just in principle? An area with more students can naturally better afford to offer programs that are of limited interest, because they will still have lots of students that are interested. An area with less students probably can't spend money on things that are only of interest to 1 or 2 students.
It's not true in either sense in the US, localized funding for schools is presented as the more fair solution.