How can I tell if an aircraft is equipped with fly-by-wire or with a FADEC?
Only an aircraft model can be fly-by-wire or not, not an individual airframe of the same model.

Designing FAA/EASA certifiable fly-by-wire systems is extremely expensive, so only expensive aircraft, produced in large numbers, are going to have it. All Airbus since the A320 and Boeing 777 and 787 airliners are fly-by-wire, so are high-end Dassault bizjets. Recently the club has been joined by Bombardier, Embraer, Sukhoi, Irkut (Yakovlev) and Mitsubishi.

This doesn't include military aircraft, though you'll largely see the same players there with the addition of Lockheed, Northrop, MiG, BAE and a few other all-military contractors. Air forces have more need for fly-by-wire and are more risk-tolerant than airlines.

The SA227 is not fly-by wire. For the most part, if you have to ask, or if it's affordable below corporate level, it's probably not fly-by-wire.

EEC (of which FADEC is the most advanced subtype) versus hydromechanical engine control choice is specific to the engine and the airframe. It's not readily visible. An airframe will either have cables and hydraulic lines or sensors and wires. The majority of jet airliners currently flying use EEC or FADEC engines.