In design, if I hit the 'Enter' key while writing text, I get this line of code (in code view)-- no problem if I leave it in or take it out, but I'd prefer to not have it not there as I don't know why it's there.
It sounds as though you have "Auto Style Application" on which is located in...
EWD > Tools > Page Editor Options > CSS
I think if you change that to Manual from Automatic it should clear up what you are seeing.
Apparently you have a default style for the <p> element "embedded" in the <head> of that document. Each time you hit the enter key on an element that is not within the parameters of the embedded CSS, I believe EWD will automagically include inline CSS to counter the default CSS. This gets a bit tricky if you are not a seasoned WYSIWYG user. Try turning off the Auto Style and see if that fixes it.
On a side note, I have a sneaky suspicion you're probably going to run into more anomalies if you are using EWD out of the box with no configuration settings of your own.