My responses are below your questions:
1) I would need to keyframe the lightning positions as well as a layer mask for when other objects would cover it up.
Yup, I understand
2) I would lose the light and color that it casts on other objects.
Well, like you say below, you could create another light with the same color and link it to the Intensity-Out and RGB-out of the lightning light, and use light linking so it only affects your chosen objects.
...after I move the plane and change my camera view, it seems to intensify the glow, which doesn't make much sense, so I have no explanation for the changes.
Weird, it migh be a distance to camera-normal issue... not sure..
Maybe there is some light linking I can do to turn off the light and reflections the plane with the background receives from the lightning light node?
Yep, I would try that if you aren't comfortable with doing this in a 3d compositor where you can control light color on only your object layers.
...Tested the paint FX and it doesn't want to make the curve paintable.
That is because the default lightning effect "bolt" is not a curve persay, it is an extruded softbody, and therefore with its dynamic connections, is not accepting your command to be paintable.
...it should still work tho... weird...
Also, are the only lightning brushes in the electric folder?
Yes.
You can tweak them to make them look, and act the way you want, as well as animate the control curve for more interesting effects as well.
Israel "Izzy" Long
Motion and Title Design for Broadcast-Film-DS
izzylong.com