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But does editing with a different interface change the rewards ? ie, if first we post with esteem app and then with say, steempeak, what is the expected behavior ?

from my understanding, No. When you edit a post, you edit the body. unless you manually change the benefactor, it remains the same.

However the edit, and the record on the block should show the app the edit was made it

No, comment options (the transaction that adds beneficiaries to a post) must be done before the first vote appears on a post. This is done immediately with the post and cannot be changed.

editing with a different interface typically does not change the reward settings and there are strong limitations on what can be changed at all, esp. once the posts have votes or replies. Benefactors, for example, can only be set once and can't be modified/extended/...