OK, then next question: What can a mage do in a dimension that does not have pylons / what kind of magical batteries are there, or are they needed? My understanding is that the lumen trees are the battery, but they need a pylon network in the same dimension to charge, and can't go into another dimension (but as I say that, can you silk touch the leaves?)
Anything to do with crafting and a lot of the utility machines require connection to a pylon network, either directly through normal repeaters, or by mini-repeaters similar to how TC's energized-node-powered machines work. There are a couple of mining machines that work with a portable battery, but again to charge the battery you need a pylon network, and are the exception to the rule.
The lumen tree exists mostly to cope with heavy load; it can store ~11 million lumens of each variety, while pylons only store 180k. I'm not actually sure what kind of load is even required to necessitate a lumen tree, because once upgraded I haven't yet been able to draw from
them pylons faster than their recharge rate anyhow.
Lumen tree leaves cannot be silk touched as they are part of a multiblock, without which they would be worthless. The luminescent battery block is the controller, which is what stores all of the important tile entity data for the tree. Even if they could be silk touched, the way the tree grows is not linear with each additional leaf; the first leaf stores only 1000, then by the second-to-last leaf ~5 million and the final leaf ~11 million, if I'm remembering my numbers right.
As for non-overworld generation, if Mystcraft is an option, Mystcraft ages will generate all overworld structures provided spawn conditions are right, except for pylons which will only generate if the appropriate config option is enabled. As of v10, assuming Reika's gotten it working correctly, Chromaticraft structural generation in Mystcraft ages will be controlled via pages instead of config, divided into plants, ores, pylons and so on. It should be noted that Nether and End access is also necessary for progression.