What's the difference between how do I look and what does he look like? Please don't pay attention to various pronouns.
In my opinion, "how do I look" can be said by a wife to her husband in order to find out what he thinks of her new dress, for example. It applies to two or more people who know one another.
"What does he look like" refers to a situation when we don't know a person, hence we ask for information about them.
I may be wrong because English is my second (not foreign) language.
Also, in the second case, by stressing the does you can give it a different meaning: 'What does he look like?' means something like 'Don't you agree that he looks ridiculous/outlandish/inappropriately dressed...'