Sorry for the late response, I had forgotten about this question.
It would, and it is an noticeable effect, but only applies at ley nodes, not ley lines. I guess larger ley lines would still manifest a slightly increased belief power, but not that much, since the energy actually needs to stay at a location in order to do anything. See it as a river of discrete packages. Each package carries energy and will affect the region it is in. However, since it is constantly moving it never stays in a location for long enough to seriously affect it. At ley nodes these packages stay longer, and would cause more intense effects.
They're important because they are what fuels the ley nodes. Without ley lines, ley nodes wouldn't exist. The two biggest impacts are that ley nodes are where Investure Cystals are found, which means that ley lines are indirectly necessary for Ritual Magic to work. The second effect is that a lot of the 'Wild' Natural Magic wouldn't really manifest anymore. Natural magic would still manifest, but be a lot more dependent on actual belief, and the level of belief necessary for Natural magic to take effect would be bigger.
If someone disrupted them, it would affect the ley nodes connected to it, reducing the power of the nodes, and probably having a bad effect on the node's local manifestations of Natural Magic. In addition the energy would need to go somewhere, which means either flowing towards a different node (I think this would be difficult for larger ley lines, since the more powerful flow would make changing course difficult) or coiling in on itself and collecting in the location of the disruption. This would cause a lot of Natural Magic to start manifesting inside of the area, and can have a number of end results (ordered in level of danger) (Note that all these effects and classifications are my own take on things, and are not canon, also, I think that interference with ley lines at this scale would be extremely difficult and would likely border on impossible):
Class I Ley Line Disruption Resolution: The energy will keep building up until the pressure allows some of it to slip past the blockade and continue its old route (though with less energy). Eventually this would stabilize and form a new ley node at the location of the disruption.
Class II Ley Line Disruption Resolution: The energy keeps building up until the pressure causes the energy to forcefully explode outwards. The disruption will vanish, or at least diminish to a weak enough version that option 1 takes effect. The issue with this is that the energy that has been building up will need to go somewhere, and will spread into the area surrounding the disruption, as well as flowing downstream into nearby nodes, meaning that all Natural Magic in a wide area around the disruption will suddenly get a large, temporary boost. The duration, range and strength of the boost will depend on the disruption, as well as how much energy has been building up and how easily it can disperse into the surrounding area (check final point, ley line formation for more info on this).
(For these sub-classes, note that for most of them the effect will lessen the further away from the epicenter you are, segueing into the preceding sub-classes)
Class II-A Resolution, Natural magic boost: All Natural Magic in the area is boosted to some degree, with people being more likely to develop abilities, and entities and objects that already have abilities will seem them strengthened.
Class II-B Resolution, Long-term Natural Magic manifestation: Reality will become weaker in the areas close to the epicenter, with Natural Magic-based phenomena materializing without the requirement for belief. Some of the manifestations can stay afterwards, and Natural magic will be stronger in this area for a long time.
Class II-C Resolution, Reality weakening: Reality as commonly known will stop functioning correctly close to the epicenter, with certain people being capable of consciously bending reality in this area.
Class II-D Resolution, Reality breakdown: The concept of reality as we know it will stop functioning in this area. Stray thoughts can drastically change the nature of reality around people and the laws of physics and common sense stop applying. In more extreme cases this will basically turn the area into a modern arts display.
Class II-E Resolution, Reality restructuring: This is an alternative to Class II-C and class II-D Resolutions, where the nature of reality undergoes a (possibly pernement) fundamental change instead of just weakening. The positive side of this is that the resultant reality is stable, unlike with other reality altering Resolutions. On the negative side, there is no guarantee that humans as we know them can actually exist under the new laws of reality.
Class II-*-C Resolution, Cascade reaction modifier: A modifier to other Class II resolutions, the energy released by the resolution has a significant impact on nearby ley lines, altering their paths and disrupting them. This can result in additional Disruptions forming, with the Resolutions from those Disruptions possibly kicking off Cascade Reactions as well, setting in motion a large scale chain reaction that can result in country or even continent wide Class II resolutions. Do note that these Resolutions would probably fade quickly and wouldn't happen at the same time, because the amount of Investure that can be trapped in Disruptions is finite, but large scale cascades can still ruin existing Natural magic ecosystems and cause widespread damage to civilization.
What do you mean with this? Do you mean the relative difference of Investure or the relative difference in how easily Natural Magic can occur? For the first one, I'd say fairly large, but dependent on the size of the ley line. For the second one, I'd say there isn't that big of a difference (refer back to point 1).
As for the locations and paths of the ley lines, I'd say it's probably influenced by both the physical and cognitive realm. The main principles would probably Path of Least Resistance, Investure Momentum, Investure Attraction and Investure Pressure.
Path of Least Resistance means that the stream would travel in paths similar to actual rivers, following the lay of the land and the cognitive realm, though it probably wouldn't fully correspond to the path of actual rivers, since there isn't a high an low point the Investure comes from and flows towards.
Investure Momentum means that any Investure is forced to stay in motion, and the more Investure there is the harder it is for it's path to change. This means that the larger the stream the straighter its path will be.
Investure Attraction means that ley lines will pull towards other places with Investure. This causes ley lines to cross with others to form ley nodes, and will also cause them to pull towards areas with lots of living beings. Taking Investure Momentum into account, this means small ley lines will often go through cities, but the larger ones probably won't since the cities wouldn't have been around for long enough to cause large effects on those ley lines. On the other hand, this means that it wouldn't be weird for ley lines to flow through large forests or islands.
Investure Pressure means that the more Investure is concentrated somewhere the harder it is to force more Investure into it, and makes it more likely for Investure to split off again. This balances against Investure Attraction, and is the reason that there are a large number of smaller ley lines, instead of all of them simply coalescing into a single large ley line.
Note: All of these are my own personal takes on them, and you shouldn't take them as canon, especially the ley line disruption resolution types (on the other hand, this could allow for some ancient precursor civilization that got wiped out because they interfered with ley lines and messed up, causing a weak Type-II-E-C Resolution that destroyed their civilization, possibly also affecting how magic works in the world (might also be an explanation for why other continents might have different forms of magic).
