"A boutique is a small shopping outlet, especially one that specializes in elite and fashionable items such as clothing and jewelry." - It is implied that a boutique sells clothes (but boutiques never sell electronics or other goods), so it's like calling it a "clothing clothes" store. I think "She has a boutique" should be accepted in this case.
I agree - that's clearly incorrect. When we say things like "she's gone" (see below), it is a tense (actually tense + aspect) construction, not possessive, as in this case. In this case "She's" must stand for "She is", rather than "She has". And "She is a clothing shop" is clearly wrong.
"garment shop" is very stilted English. We might more readily say clothes shop (or store), dress shop, outfitters or even boutique, but absolutely never "clothing boutique" as in English usage boutique ALWAYS means a clothes shop, though not for the kind of clothes this unfashionable middle aged male wears!
Maybe where you live, but if you read the other comments you will find there are other kinds of boutiques--I have a friend with a jewelry boutique and if you google boutique banking, you will get many hits. For me, a boutique is an establishment that sells specialized goods at high prices.
In "boutique banking", "boutique" is used as an adjective, which it definitely can be. But "a boutique", a noun, as in this case, is necessarily an upmarket clothes shop in British English (though in American English it appears it's just an upmarket [anything] shop). Therefore, this should be an accepted translation because British/Commonwealth and American versions are both accepted in the course.