Are these verbs related?
I noticed a certain pattern among Hindi verbs - some verbs seem to be similar, as if related both in the meaning and in etymology, for example:
die मरना - kill मारना
see देखना - show दिखाना
read/study पढ़ना - teach पढ़ाना
walk चलना - drive/run (a business) चलाना
Is there a real basis for this intuition? Are those what you call causative verbs?
Your intuition is correct. Given a Hindi verb, you can find others with the same root that have related meanings.
For example, in your first example, मरना (to die), मारना (to kill), मरवाना (to get someone killed). The third form is the causative because you are having someone else do the action for you.
Similarly, in your second example, देखना (to see) दिखना (to be visible) दिखाना (to show) दिखवाना (to get someone to show). Again, the last is the causative.