Three paths to victory: reach 99% of world GDP (economic hegemony), reach 70% of world military power, or bind every country to you (total influence). The Statistics tab shows where you stand in the world rankings.
Your regime sets the election calendar (every 4-5 years in most democracies): if your approval is below the threshold on election day (40-60% depending on difficulty), the game ends. The election date is shown in the info bar — invest in satisfaction as the vote approaches.
Through economic pressure: buy the facilities of bankrupt countries (whoever buys, owns), make production chains dependent on you, pull their population with migration. A country whose facilities you largely own becomes your economic satellite in practice.
Yes — choose Continue on the victory screen and keep ruling the world in free play. Achievements and personal records keep accumulating as you play.