Translation:Where is the hospital's entrance?
Based on other discussion pages, it would be best to consider どちら as a "Which way" more than a simple "Where". However since both どこ and どちら can also mean "Where", どちら can be considered the more polite version.
I wrote 'Where is this hospital's entrance?' and it was marked wrong. Is there really a big difference between my answer and the right answer or is what I wrote incorrect in English?
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!
This is getting frustrating！I type the correct Kanji characters and I get marked wrong? Come on! "病院の入り口はどこですか."
Is 入口 usually pronounced as fast as the duolingo speaker? Almost sounds like illguchi
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