Translation:Where is the hospital's entrance?
They probably want you to be more careful about using "this" since that would be translated differently. In practice, not really a different meaning in this case, but learning the language properly means being precise about what you're saying, so you get it right when it does give a different meaning!
Yes, it is pronounced "iriguchi".(iri +kuchi=iriguchi). There are certain rules about pronunciation changes... it usually happens with compound kanjis (jukugo?) Here is a link if you're interested: http://www.genetickanji.com/docs/pronunciation-change-rules-japanese.html
I put びょういんの入りぐちはどこですか。I can hardly believe Duolingo didn't accept it. I mean the exercise was to type what I heard, not to type all the kanji that one would normally type.