With a freshly filled pool with no cya, it is almost impossible to keep chlorine in the pool. For the first week or so, you will most likely need to add bleach 2 or 3 times a day. After you get some cya in there which will take about a week to dissolve completely, you'll be able to test and dose with bleach in the evenings only. I can't comment on how much Borax to add without knowing your volume, but to answer your question about how to add it ---- you can pour it slowly into the skimmer while the pump is running, breaking up any clumps. It will not stain your liner.

Give us the details about your pool please -- size and volume and also tell us what type of filter and size the pump is.