For example, I can change whites and blacks in the “Basic” box. But I can also do that in the “Tone Curve” box. Thus I’m wondering if I should use both boxes(meaning they are complementary) or if using only one of them is sufficient because they actually do the same thing at different level of precision.
There are lots of tools in Lightroom that overlap and often there are multiple ways to do the same thing. Depending on what you are trying to achieve or how you prefer to work, you might use one instead of another or many different settings to hone in your desired result.
In your example, you might set the white and black point, then later, decide that you want to bring up a band of shadows slightly. You could try and do this using the shadows setting, but it might be that using curves allows you to get there quicker and more intuitively. It is often the case that you will use one control to get you to the ballpark and another (or others) to refine.
Once you've been using it for a while and are familiar with the different controls, you will find your own preferred workflow and feel intuitively which tool to use for which situation.
You always have the histogram as a source of truth, so whatever you have done with multiple settings, it will show you clearly the effect any changes have had.