Learn Turkish: Ben iyi bir hemşire miyim?

It is made of three parts! First is the question particle mi. Next, we add the "I am" suffix, which is -im. Because mi ends in a vowel and -im starts with one, we need the buffer letter y between them. This gives us miyim.

Why is the question word miyim written separately from hemşire?

In Turkish, the yes/no question particle (mı/mi/mu/mü) is always written as a separate word from the word before it. However, personal suffixes (like -im for "I") attach directly to the question particle itself. So it is hemşire miyim? and never hemşiremiyim? or hemşireyim mi?.

Why is it iyi bir hemşire instead of bir iyi hemşire?

In English we say "a good nurse", but in Turkish, when you use an adjective (like iyi) and the word for "a/an" (bir), the adjective almost always comes before bir. It literally translates to "good a nurse".

Do I have to say Ben at the beginning of the sentence?

No, you can just say İyi bir hemşire miyim? because the -im at the end of miyim already tells us the subject is "I". Using Ben just adds a little extra emphasis to the sentence.