Bearing in mind the tests you have already done, with the engine running, if you remove one spark plug at a time it should be possible to tell which cylinders are not firing because disabling the non firing cylinder will make no difference to the way the engine runs.
If you have sparks on the discovered cylinders then it may be down to a fuel blockage in some injectors because you say that you heard all the injectors clicking.
If it turns out to be the injectors they can be tested/serviced in the workshop according to some notes on the PDF to be found here:
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or you can replace them or they can be professionally cleaned.
New Theory.
Now as to the backfiring in the exhaust this indicates unburned fuel/air self igniting when the hot gasses from other cylinders are exiting. That would indicate that you have do have a spark problem on 1 or more cylinders.
OR
one of the injectors is stuck open (yet still clicking) so the flooded cylinder does not fire but the fuel/air in the exhaust system is self igniting.
For ignition problems dont overlook the ignition amplifier which can go wonky before it completely gives up the ghost.
Good luck