The chances of dying on a single airplane flight with a major American or European airline are roughly one in 53,000,000. These are about the same odds as those of winning a Powerball lottery jackpot.
You need not worry about falling to the ground, even if the engines stop (which they never do). Airliners can easily glide, even without engine power, and in fact they glide down to the destination airport on every flight, after the engines are set to idle (gliding down with the engines idle is the most fuel-efficient way to descend).
Engines are designed to tolerate ingestion of average-sized birds. A flock of large birds can shut down the engine, but you won't be meeting these at 36,000 feet. Bird strikes occur mostly during takeoff or landing. In most cases, the engines dice and roast the birds and spit them out the back.
International flights are no more dangerous than domestic flights. There's a certain psychological impact to flying over water, but the airplane doesn't care whether it's flying over land or water. Water doesn't make the engines any less reliable, and they are very reliable.
Engines are so reliable, in fact, that many airline captains today go through their entire careers without ever encountering a mechanical failure in a jet engine. They practice for them in the simulator, but they might never see one in real life.