Add the Borax. It does a much better job than soda ash. Soda ash is sodium carbonate. CYA is cyanuric acid and will lower pH, but not as much as muriatic acid.
Yes, get the drop-based test kit from Walmart, or the Taylor K-2006 kit from the pool store. Ben's PS234 testkit will do everything you need for testing. We here find test strips to be very unreliable, and some of only use them to get ballpark figures.
Hope this helps.