Why does te ha ikenai use ha? I know its a construction, but where did it come from? Te form verbs are not nouns, it doesn't make sense to me that ha could be used with them.
THe は in ～てはいけない. Is actually not the topic marking particle, but a different particle entirely. IT's kind of like how the particle に has a number of different uses. In this case the は is used to emphasize the negative part of the sentence. You'll see in other places が being replaced by は before ない or another negative verb or adjective.
Edit: I found some more information on the subject. This website does a good job discussing this concept as I understand it.