ты думаешь - informal singular
вы думаете - plural, or formal singular/plural
Also: These are NOT the imperative forms of the verb; those are (Imperfective aspect):
Don't ask me what Imperfect Aspect means - I haven't gotten that far yet; I'm merely copying these verb-forms from a conjugation table, and I think it's a good idea to get things right the first time, even if you don't yet know what they signify.
Looking at the Russian and English as I see them at the top of the page--
"Думаете, у неё есть ответы?" Translation: Do you think she has answers?
--I would say no. "Do you think has she answers" would not be correct English.
You could make the case that a standalone sentence, "Has she any answers?" or "Has she the answers?" would be correct - note that it sounds more formal to my ear, and would be probably used more widely in British English rather than American English. (I do not imply that one is more correct over the other - I am simply distinguishing regional differences as I see them as a matter of trivia/interest. Both uses would be perfectly understood in either location.)
However, the main part of the English sentence is, "Do you think", with an understood/omitted "that", followed by "she has answers" at the end. So in other words, the main clause is Do you think, followed by the subordinate clause, [that] she has answers. Subordinate clauses that start with that (or clauses which could use that but omit it) do not use inverted word order such as "has she" and instead must say "she has." Inverted word order is when the verb precedes the subject of the sentence.