An interrogative phrase How replaces the preposition phrase including any prepositions:

• How [does it look like something]?

An interrogative phrase with What just replaces a noun phrase:

• What [does it look like something]?

So, in short, the Original Poster's intuitions are correct.

An interrogative phrase How replaces the preposition phrase including any prepositions:

• How [does it look like something]?

An interrogative phrase with What just replaces a noun phrase:

• What [does it look like something]?

So, in short, the Original Poster's intuitions are correct. If we try to use How but not delete the preposition, the sentence will be ungrammatical:

• *How does it look like? (ungrammatical - like should be deleted)

An interrogative phrase How replaces the whole adjunct including any prepositions:

• How does it look [like something]?

An interrogative phrase with What just replaces a noun phrase:

• What does it look like [something]?

So, in short, the Original Poster's intuitions are correct.

An interrogative phrase How replaces the preposition phrase including any prepositions:

• How [does it look like something]?

An interrogative phrase with What just replaces a noun phrase:

• What [does it look like something]?

So, in short, the Original Poster's intuitions are correct.