UC admission questions

Do UC’s admit applicants by their major or do they admit them and look at the major after?
What should an alternate major for Computer Science be? (I was thinking about applied mathematics or economics)
Do the college board’s 4 free applications stack with the UC’s 4 free apps? (My household income is very low)

Each UC admits differently. For example, UCSD admits into the University first and then into the major. UCD admits by major into their College of Engineering but in their School of Biological Sciences, they admit by college. See below:

Admission decisions are made based upon the qualifications of the applicant pool and the number of available spaces within each academic area:

-College of Agricultural and Environmental Sciences admits by college
-College of Biological Sciences admits by college
-College of Letters and Science admits by division within the college
(Humanities, Arts and Cultural Studies; Mathematics and Physical Sciences; Social Sciences)
-College of Engineering admits by academic department
-Students applying as “undeclared” or “undeclared/exploratory” are considered within the college/division to which they applied.

In general, if CS is in the Engineering department, most will admit by major. Also, CS is capped/impacted at several schools, so picking a non-impacted major is usually recommended or you face being accepted as Undeclared and trying to switch majors later can be extremely difficult.

Regarding Fee waivers, you can use the 4 for the UC’s but the CB waivers cannot be used for an additional 4 UC’s. Other schools will accept the CB waivers. See link:
https://bigfuture.collegeboard.org/get-in/applying-101/college-application-fee-waivers/participating-colleges