Is this typical for the Present Simple?
Your examples are good English and sound quite natural.
The simple present is used relatively rarely in English. If something happened even two seconds ago, we use the past. "I was really surprised when I saw you walk in this room." Past tense. We use the present for something literally happening at this instant, like "I am happy to see you." You are being happy right now. We mostly use the present tense for ongoing action. "I love chocolate." I probably loved it in the past and will continue to love it in the future, but I love it right now.
I don't think sit, lie, and grow are particularly special in this regard. In the specific sentence that you are using for your example, "while I X here watching waves", the words that make sense to fill in for X are limited, not by some rule of what words can be used in the present tense, but rather by what goes with "here" and "watching". It sounds natural to say "while I sit here watching waves" because sitting and watching go together. "While I talk here watching waves" doesn't work because talking and watching do not go together in the same way. But you could easily save the sentence just by adding an "and": "while I talk and watch waves".
Almost any verb should fit in the general construct, "What are you doing while I X?" "What are you doing while I read?" "What are you doing while I eat?" "What are you doing while I paint the room?" Etc.
In general, the present tense is appropriate here because you are asking mom what she is doing at this very moment, while you are doing this other thing. If someone called on the phone and asked what you were doing, you would use the present continuous, "I am sitting here watching waves." Or if you had gotten up to get to the phone so you were no longer sitting, or if you don't think of yourself as watching the waves any more because this person has interrupted you, you would use the past, "I was sitting watching waves."