It seems that usage of "выглядеть" depends on what part of speech it needs to be conjoined with.
1. Выглядеть + как + Noun phrase in nominative case
The expression is used to show that something/someone looks similar to something else.
выглядит как королева - looks like a queen
выглядела как английская королева - looked like an English queen
выглядит как новый - looks like new (the noun is dropped)
2. Выглядеть + Noun phrase in nominative case
This form is used in questions with "как", or in statements with "так." In the latter case it simply states the facts. It is the only use case which does not use similarities.
Как выглядит траектория? - How does trajectory look like?
Так выглядит спутниковая антенна. - This is how satellite antenna looks like.
3. Выглядеть + Noun phrase in instrumental case / Noun phrase in instrumental case + Выглядеть
Similar to the first case this expression is used to show that something looks like something else. There is no difference in meaning between the first case and this one.
выглядит новобранцем - looks like a rookie
выглядит смешной пародией - looks like a funny parody
выглядела бледной и блёклой - looked pale and dull (the noun is dropped)
Островком роста выглядит страхование имущества. - Property insurance looks like an island of growth (the noun phrase in instrumental case can precede the verb)
4. Выглядеть + adverbial phrase
The expression is used to show similarity. Just like the first and the third cases.
выглядит странно и неубедительно - looks strange and unconvincing
Он пытается выглядеть как можно умнее - He tries to look as smart as possible (adverbial phrase uses the word "как")
Моей дочке 13, но она выглядит на 15 лет. - My daughter is 13, but she looks as if she were 15
In short, the form that needs to be used is dictated by what part(s) of speech is used in the rest of the phrase.