For reasons that have been covered in otherthreads tyre pressures actually vary just a tiny amount whwn the carried load changes, so asymetric loading has no significant effect of tyre pressure.
Temperature certainly does, but its difficut to establish the internal air temperature without specialist eqeuipment. The surface temperature can be very different to the internal, so touching the tyre is not a good way testing tyre temperature.
Tyre manufactures are not daft, and of course they know that a rolling tyre carrying a load will heat up. It will be influenced by the ambaient temperature, but also by heat generated by the friction of the tyres materials as they flex under load. They will have tested their products to make sure they withstand the amount of energy that is used to heat the tyres in usage, and the resulting pressure and temperature gains for the conditions they are designed for. For example winter tyres have a rated maximum ambient temperature above which the shouldnot be used. and all tyres have an optimum static pressure range covering a static load range neither of which should be exceeded.
Ideally tyre pressure should be set accurately, but there will be variation in the accuracy of pressure gauages. It is not uncommon to find a 10% difference in readings between gauges, it seems Trading Standards do not now regulalry test them, so it's effectively impossible to know how accurate any of the domesstic or garage gauages are. But we dont see cars falling off the road all the time, so it is reasonable to assume margins of 10% are not significantly dangerous.
I would suggest that whilst absolute pressure accuracy woud be ideal, what is probably more important is consistency of pressure for tyres on each axle.
No type of gauge that is not calibrated can be considered more accurate than another, but digital gauges will normally resolve to a smaller unit thus making reading easier than analog or pencil gauges. Consistency is equaly important, and some gauges will exhibit a hysteresis effect, where it may give a different reading for the same presure depending on whether the pressure is rising or falling. The trick is to always use the same metheod to check the pressure for example always slightly over pressure the tyre and bleed pressure to bring it down to your target value.
Some electric pumps will switch automatically when a preset presure is reached.