Do they hold democratic elections in Panama? And is it a president or a prime minister?

Panama is indeed a democratic republic, with a president elected by popular vote, unlike the US’s electoral college system.  The Panamanian president is both head of state and head of government.  The president is elected for a five-year term, and can’t serve two consecutive terms; rather he/she must wait at least two terms, before running for re-election.  Panama is also one of the few democracies in the world to have elected a woman president (Mireya Moscosa, 1999-2004).