No, there isn't any thing like as you have described in (1), I think you are pointing toward the current consumption of devices. Except the BJT devices. Mosftet,JFET and OPAMP have fet input stages, even controllers have fet stages. So they require very low current as an input.All the computational devices that we use like ICs and in discrete component are low powered. So you may see a trend in low power devices that have high input resistance and computational abilities, rather than power devices diodes, bridges, thyristors. We interlink small power(computational devices) to high power devices, like brain operating our body.So you might have seen low powered devices with high input resistance. In high powered devices they have low input resistance.
As far as triggering is concerned, I'm not sure about this whether there are different types of C,HF,LF. When I work with oscilloscope, I haven't come across such thing. About triggering, I used to adjust the vertical knob.Actually it's like when you talk about triggering, there is a signal(Most probably a triangle) by which it compares with the signal coming in the oscilloscope, there by at a point the two waves intersect each other, so you see a sustained wave. So by adjusting the triggering condition you can adjust your wave accrodingly. As far as C,HF,LF is concerned. I think they are built in the oscilloscope probes, because oscilloscope probes comes in wide variety for specific application,people use variety of probes accroding to their application need. Coupling would be done in probe themselves. As often probes have 1X and 10X feature.