Well, I'll address these one at a time.
1. Any magic user or energy worker, just from experience, knows that continuious use of their own energy makes them tired (meaning in a single session). Rest brings that energy back. Also, bringing in energy to themselves, removes the lethargy(in most cases). This issue has been tested and retested by many traditions, not just omnimancy. As far as a person generating energy, they do, however, that doesn't mean you generate energy at the same rate or greater than you use it in spell work. 99.9% of the time, its the opposite (you use far more energy than you are generating). (Hence the reason for many traditions to have group workings to counter the spell energy load by distributing the power requirements among the participants). Take blood for example. You can lose blood without requiring a transfusion to replace it. That blood will regenerate over time. However, if you lose blood TOO quickly, the person dies, because their own means of regenerating blood can't keep up with the rate demands of the blood loss. Generally speaking, when one uses one's own energy, it's more considered from a pool of energy, rather than a fountain since the regeneration is far to slow to be practical for spell working to be considered a fountain of energy. It just happens to be a pool that regenerates over time.
2. Ambient energy is "discarded" energy from a variaty of sources intermixing with each other. This can include living things (energy expelled from their auras), to more "natural" energy sources, like fire, chemical reactions, light, polar magnetics, etc. The list is far too long and wouldn't be complete anyways. Each can do a lot of release or almost completely negliablable release of energy. However, over LONG periods of time, it builds up. The MAIN source is living entities (which would even include spirits in this case too). That just shows where this random energy comes from. The reason why it's considered "weak" is because it's not concentrated enough to be immediately usable for spell working. Meaning, extra effort needs to be done to gather this energy and forceably concentrate it into a usable density. Think of all the water vapor in the air. Massive amounts of it is all over the world. But people can't drink from it. Not unless they find some way of collecting it and concentrating it to liquid form, and this takes time. Not that it's hard, but it is an extra step that you MUST do before it's usable. So ambient energy can be like that water vapor. It can be gathered and used, but it can take a lot of effort to collect enough to have enough to be worth using, because the volume involved is so small.
3. Ley Lines are "alternate power sources", because the majority of traditions/systems, personal energy is used rather than external energy(external energy= any energy that isn't generated by the caster). Either they don't acknowledge external energy or use energy from another being (either other participants, and/or diety/elementals/entities/etc). When a spell is cast, it defaults to the person casting it as it's power source. The caster must specifically tell the spell NOT to use them as a power source but if they want it powered off of something else. (Even if those specifics are hidden in the subtext of the ritual itself, if your doing things that way). Ley lines are just naturally occuring pools of energy from ambient energy. Just like the example above, water vapor will naturally condense over time and form pools where the environment dictates is easiest. (Ie. water will pool in lower areas that have a "bowl" to contain the water, even if that bowl is the size of an ocean.
) Ley lines have different criteria for what makes them pool, but they pool non-the-less.
4. The same way as someone in the "country" would to find a ley line. Please see the tutorial document. There can just sometimes be less ley lines in cities but by no means are not present, and in some cases can have just as many. The "flavor" of them will be different (from an farmland/forest set) simply because of the type of energy that normally fills them. So many might be missed simply because a person might not be as sensitive to certain types of energy than others (at least for magical workings).
5. A concentration tether is what we term also as a "maintenace" tether. Generally speaking, when a person casts a spell, and therefore is powering it, the power tether and the maintenace tether are part of the same tether going to the spell in question. A spell requires power to run (ie. power tether in this case), and requires something to maintain it's cohesion. At least long term spells. To form a spell, requires concentration (after a fashion depending), and a VERY small amount of concemtration of the individual is required to MAINTAIN that spell. Normally it's not even noticed, especially since the power draw usually FAR outweighs the slight draw of the concentration tether. However, when you start using other power sources than yourself, you will end up noticing that there is still an "upper limit" of how many things you can have going at once, (which is FAR more than if you just had everything powered off of you mind you). You really have to have a LOT of things running at the same time to hit that limit, and we never have, but we have gotten to the point of seeing an effectiveness fall-off, which we resolved via a different method that I won't go into here. The main purpose of a concentration tether is to keep tabs on your spell, to maintain your spells cohesion, and depending on the nature of your spell, send back information (even if it's just a status update). You've might have heard of people being able to "feel" their spells, and if it got canceled or what it's doing. They are doing that via their concentration tether. It's just the mechanics of what is going on, which we in Omnimancy are always interested in. In the majority of cases, it's not even needed to be known about.
6. Star energy is simply a different source of energy, as opposed to people/entites, and other naturally occuring sources (see above). Stars are giant fusion reactors. Part of the energy it produces is magical. Magic users have been using the sun as a source of power either symbolically or litterially for ages. The Sun is just another star. If you get strong enough to tap effectively into other stars, then that's more power to use. In our experience, stars will put out a LOT more usable power than a ley line will. So as a general rule, if you can get to stars and use them as power sources, you normally don't use ley lines anymore. However, power from a fusion reactor like a star is a different "flavor" than what might come from a ley line. If your magic is very strict about the type of energy you use for certain things, then it may not be as useful (although you can always put filters on). It certainly won't have the "organic/life" feel that ley lines will, since ley lines are generally formed from the excess OF life, where stars are not. As far as what Star energy is used for, well, spells that require or benifit from that much power, which is true in most applications.
I hope that has answered your questions.