For a trip to be in my country of origin does it have to start and end at it? If the trip starts at my country of origin and ends in another country does it count as a normal travel day?
You can choose when you want to use you 2 travel days in your country of residence. They can be anytime during the validity of your pass and don't have to be at the beginning and the end.
I want to go from Seville to Barcelona on day 1 and Barcelona Paris on day 2. Does the 2nd day count as trip in the country of origin (Spain) ?
Yes, it does. If you do it like that, you will use both of your travel days in your country of residence. If you need more, then you'll need to buy normal tickets.