What are the main components of the Airbus fly-by-wire system? Is ECAM related to FBW?
ECAM and FBW are not directly related, but information and alerts regarding the flight control computers and actuators are displayed on the ECAM screens, like any other information not visible on the primary flight display or the navigation display.



Fly-by-wire

The fly-by-wire concept is actually simple:


In traditional aircraft, the control surfaces like ailerons or elevators are linked to the control inputs used by the pilot, e.g. the column. This link can be direct (cable) and/or amplified (hydraulic or electric actuator commanded by the pilot).

  
In "FBW" aircraft, the control inputs are instead sent to calculators which deliver actual orders to actuators. Each FWB system, in addition to introducing calculators into the pilot-control surface chains, also gets information from sensors to measure the aircraft response to orders (feedback).





This design has two advantages:


There is an actuator (e.g. an hydraulic jack), so the pilot (or the autopilot) has to exert on the control inputs only a fraction of the actual force that needs to be exerted by the actuators on the control surfaces.
More important for the concept, the calculator can supervise the pilot commands, so that the aircraft is never put in unwanted or dangerous configuration, e.g. stalled. This system is similar to the full authority digital engine control (FADEC) used for the engines.


The main calculators for Airbus A320 family are:


ELAC: elevator and aileron computer
SEC: spoiler and elevator computer
FAC:  flight augmentation computer
SFCC: secondary flight control computer


They are redundant and some functions dedicated to one computer can also be executed on other computers.


Source: Fly By Wire Systems Explained

Actuators are moved using a transfer function from pilot input. In simple words, some correspondence links the actuator deflection to the pilot input. These correspondences are usually named "flight control laws". Airbus uses 3 laws:


Normal: When everything needed by the calculators is available. Maximum protection is available. Sidestick inputs by the pilot are converted into vertical G-load demand and lateral roll rate demand.
Alternate: When some calculators required data are not available. Some protections may be lost and sidestick lateral inputs are converted into a direct equivalence in control surface deflection angle.
Direct: When no protection can be provided by the calculators, due to calculator failure, missing input, actuator or control surface failure. Vertical and lateral sidestick inputs are directly converted into a proportional surface control deflection. Basically the aircraft is a non-FBW aircraft.




ECAM

In parallel instruments in general have evolved from gauges to electronic displays. The elimination of the third crew member (the flight engineer supervising engines, fuel and other parameters) has led to automatic supervision of aircraft parameters and filtering of displayed information.

By default, only a few parameters are shown to the crew, other are replaced by alerts when something is unusual or requires attention. The crew has also the possibility to display parameters/status on demand, e.g. the status of the cabin doors or the fuel tanks. The electronic centralised aircraft monitor (ECAM) is just such system which monitors and displays alerts and important parameters.


A319 ECAM after an actual electrical failure, source

The ECAM system includes two displays that can be configured by the crew:


Source



Relation between FBW and ECAM

Airbus FBW reconfigures laws when one of the flight control computers has failed. Because knowing this reconfiguration is vital for the crew and it follows some failures, this leads to alerts, information and suggestions being displayed on the ECAM screen. However this use of ECAM is not particular to flight control computers.


ECAM indication of autopilot being off, and laws being changed, source

For more technical information about this topic, see question: Is a Control Law Degradation in Airbus Planes displayed on the ECAM?