1. The Rishonim obviously thought they themselves were Achronim. Rashi and Rambam thought they were utterly contemporary, modern authors .
2. There is no strict rule. As with all historical classifications, it is subjective.
3. A border of around 1500 seems logical. Before you had a big kehillah and Spain, and afterwards Sefardim were those who had left Spain. Among the Christians, this was the end of the medieval period and the start of the modern period (rise of nation states, Preotestants, etc.). Among the Muslims this was the period where the Turks (rather than the Arabs) rules the Middle East. It was the period in which printing became widespread – and that was a major technological change that affected us more than most, since most goyim were illiterate.
4. Over time such definitions would likely change. If you wait long enough, we’ll probably be considered Rishonim. Playing with the dates that periods began and ended in history is something historians love to do, especially with sufficently strong beverages to encourage discussion (meaning it is about convenience, not substance). I would argue that the period of the 1940s is a major “watershed” in Jewish history, and everything before 1940 is the “past”, and post 1950 is the “present” – and maybe in a few centuries people will see it that way.