All the manuals state that heaters should be run monthly. No one appears to RTFM!
First thing that I would be looking for on a marine installation is corrosion anywhere, thermostat/ecu/motor. Symptoms sound a bit like the motor brushes are worn out/stuck - if the resistance is incorrect start up will not happen, intermittent contact could be happening.
Regarding number of attempts - the heaters should make an attempt to start, if fail it should then make a second attempt on its own - this is where the number of attempts doubles. You do one start up the heater does two and so on. ( Some heaters have no lockout, some after 3 attempts and others 5 )
Don't listen to anyone who tells you to apply a constant 12v to pump, they don't know what they are talking about and will possibly burn your pump out for you.
Mocki has got the heater fuse at the wrong end - it should be at the power source end, possibly a fuse box in that set up as I would expect to see a hefty main cable to the instrument area.
Motor fuse should be in the ecu - if your ecu has one there should be a cap on the bottom and a diagram with the fuse rating printed on the face of the ecu. They don't all have a motor fuse.
Transducer quite often fails due to a nick in the cable sheath, water can fill the coaxial screen which then messes up the signal.