Using dass in this sentence creates a kind of "sub-sentence" where the word order follows different rules (dass is called a subordinating conjunction). Here's a lesson on it: http://www.bbc.co.uk/schools/gcsebitesize/german/grammar/conjunctionsrev2.shtml
"Du siehst, dass die Ärztin langsam isst" (You see that the doctor is eating slowly) sounds just the same
No - it's feminine, singular - a woman doctor. English can't say that without the extra word.
Is my answer, "you see, that the doctor is boring" not technically correct? I think I remember my German professor telling me that "langsam" means boring when applied to a person. "Ich bin langsam" - I am bored. "Er ist langsam" - he is boring.
No, it's not usually translated as that. Just "doctor" is fine, as that is the typical expression in English.