If all of your college credit is lower division non-UC courses (all community college courses are lower division), then it will be capped at 70 semester or 105 quarter units, and will not put you at risk of having too much college credit to transfer to a UC. Even if you go over that unit limit, all courses taken will count as subject credit to fulfill specific course requirements. See also http://talk.collegeconfidential.com/uc-transfers/2081175-uc-transfer-faqs-part-2.html .
Yes, you should complete as many major and general education requirements as you can before transfer. CS is a major where many UCs have specific courses that are not covered by most community colleges, so that you will have to “catch up” after transfer. Having completed everything possible before transfer reduces how crowded your schedule after transfer will be, allowing you to take more electives later.