First:
German does not have those lean construction like for + verb-ing or verb-ing, I verbed something else. You have to make normal subordinate phrases for most of those. The options here would be:
Ich danke Ihnen dafür, dass Sie mich dieses Wort gelehrt haben. I thank you for that, that you taught me this word. (lit.)
Unless the word can cure cancer this is definitely too polite though :). The toned down version:
Danke, dass Sie mich dieses Wort gelehrt haben.
lehren is also very polite and formal in this example, so to tone it down to every day German:
Danke, dass Sie mir das Wort beigebracht/erklärt haben.
Second:
Vater, lehre mich...!
This is an order, thus it doesn't really have a grammatical subject in the sentence. Vater is a pretext to address your order, mich is accusative case of I.