One of the advantages of using river sand is its excellent drainage qualities, but as long as what you're using is finely screened and levelled, it shouldn't be making your bumps worse.
Scalping is simply caused by removing too much of the grass length at once and exposing the stems. If you're confident that you're only removing the top third of the lawn when you mow, it's fine. The thatch layer is the build up of dead material and runners that is between the soil and the actively growing grass on top.
As for the watering, an inch or so once a week is usually enough. The key to building a strong and healthy root system is to water deeply rather than regularly. This encourages the roots to grow deeper and increases the drought tolerance of the grass. Anything you can do to improve the health of the grass will not only improve the appearance but also it's ability to resist disease and pests.
Start with the PH test and I'll keep an eye out for your pics.
