Why does Iago completely mess up Othello's happiness and get Desdemona wrongly murdered? A good question.
Basically, he does it because he is a bad man. A very bad man in fact. In modern language we would call him a complete psychopath. He is very good at being charming, friendly, sensitive, intelligent, caring, understanding, sympathetic etc etc. He knows how to be a good person, but he only gives a surface show of goodness and underneath he is an extremely dangerous murderer and trouble-maker.
He gives some reasons for his actions...
1) Othello may have slept with Iago's wife.
2) Othello made Casio his lieutenant instead of Iago.
3) Iago hates Othello.
4) Iago may be jealous of Othello having Desdemona
The play is set in Venice and Cyprus because in 1600 The City of Venice was very very powerful and owned lots of territories. Cyprus is an island near Turkey and Greece. It is strategically very very important for controlling Mediterranean trade routes. Historically it changed hands many many times and is still a cause of deep argument between Turkey and Greece who both claim it is theirs. In the play, Venice controls Cyprus, but the Turks are threatening to invade, so Othello and a Venetian military force are sent to Cyprus to strengthen it from Turkish attack.