as long as you clean any dust filters and use some compressed air for the vent holes occasionally, you should be fine.
Personally, I always remove dust filters because they plug up easily and can cause the system to overheat. I'd rather have a bit of dust on the PC components instead of impeding proper airflow through the case.
Also, be careful using compressed air because it can spray liquid refrigerant. It's typically not a problem since it evaporates quickly but could still damage smaller components if hit directly.
Use a regular air compressor or one of those handheld plug in kind if u have it - and don't forget to hold the fans in place whilst doing the air blasting, otherwise it could ruin the fan bearings.
Heat does increase resistance just as cooling decreases it, in fact get something cold enough and it becomes a superconductor, but the extra heat from dust probably doesn't significantly alter the resistance, but I've never tested.
yeah the biggest thing with dust in a PC is just impeding airflow, and with a significant amount of gunky dust like what was shown in the pic it's more like an insulator for the components, which definitely isn't good lol