Transfers by major | University of California can give you an idea of admission difficulty to various UCs and majors. Note that UCs generally only admit junior-level transfers (i.e. those who will have 60 semester credit units by the time of transfer, are ready as possible to enter a major, and have completed base course requirements and as many major-prep courses as possible). Most transfers come from California community colleges.
Getting California residency for tuition purposes requires that you and your parents reside in California for 366 days, as noted by @Gumbymom above. Out-of-state tuition at UC is very expensive, and there is no need-based financial aid for non-California residents.