This is a very fast op-amp and it's not unity-gain stable: it won't work correctly at gain 1. It needs a minimum noise gain of 25x for stability. Such op-amps generally are incompatible with solderless breadboards. For add-hoc prototyping, dead-bug them on a solid ground plane.
The output on pin 6 is at -0.52 volts when I let both pin 2 and 3 float.
The output voltage in this condition is irrelevant, since the op-amp is not specified to work correctly in such circumstances.
changing the trimmer nothing happens to output on pin 6
Are you measuring with a voltmeter that has resolution of 10uV at least? If not, then you won't see much, because the entire trim adjust range will move the output a couple mV.
Recall that the trim terminals on op-amps are only to be used for trimming the op-amp's own input voltage. They must not be used for any other purpose.
Since these parts have small offset of just +/-1mV, to use the offset trim you should be able to measure the input offset with 1uV resolution - the voltmeter is across the input terminals while the op-amp is configured in the application circuit, and properly biased. Then tweak the trim potentiometer until this input voltage is down to 0uV+/-1uV. If you have a 10uV resolution voltmeter you may still do it, but that voltmeter better also have a comparable accuracy.
Misadjusting the trim potentiometer makes the op-amp perform worse. So, you must be able to measure initial offset and then be sure that you brought it down to zero.
The trim potentiometer cannot be used for trimming out any voltages external to the op-amp itself.
If your application really calls for a 1x gain difference amplifier, and not, say, a 25x difference amplifier, and you have to use the non-unity-gain stable LT1226, then you have to bump up the noise gain to 25x, by using the circuit below. The 1k resistors have to be matched to 0.01%. The 24 Ohm resistors have to be matched to 0.01%, but the match relative to 1k resistors can be 1% and is not critical, as long as the resistance is kept below 24.5 Ohms, to maintain the noise gain of 25x minimum needed for stability.

simulate this circuit – Schematic created using CircuitLab
Another way of compensating at low gains would be to use lag compensation, but that requires verification on a test bench.