The timing video was a pretty fair explanation of the matter, if a little jumbled, and the timing numbers he was using are off quite a lot compared to what actually gets used in real life.
The A/F video explains stoichiometry (the chemical balance of having the precise amount of both oxygen and fuel required for combustion) better than it does anything else, but makes little or no mention of the effect it has on performance when you fudge either way.
Ignition timing requires "lead" or advance, because, as pointed out, you want the building pressure of combustion to reach a point at which it is applying maximum pressure on the piston as the crankshaft reaches the most mechanically advantageous zone of rotation. That zone begins at around 15 degrees ATDC and peaks at around 75-85 degrees ATDC depending on geometric factors like rod length vs. stroke, bore offset if any, etc. Because the piston spends very little time between TDC and 20 degrees after, ignition advance is required to let the burn "get a head start". The real number in an engine with cylinder units like a YZ450F has is usually in the low to upper mid 30's BTDC.
Basically, if the flame is too late (retarded timing), it puts less than optimal pressure down on the piston. If it gets started too early (advanced), it can develop enough pressure to actually slow the piston down as it approaches TDC, which obviously causes a loss of power. In practice, this last condition will usually be accompanied by some level of detonation.
Detonation means that the unburned portion of the fuel spontaneously ignites, all at once, instead of the smooth wave of spreading flame that it is supposed to produce. This normally happens at a point after normal ignition occurs, and is caused by the heat and pressure of combustion rising to a point where the remaining fuel ignites from that instead of contact with the advancing flame. There are other causes, such as pre-ignition (ignition by an unintended source at a point sooner than the system timing point), but they don't bear on timing for the most part; they indicate other problems.
What happens when you add ignition advance with the tuner depends on how closely the timing was to optimal in the base map at the point being mapped. Since you can, let's say, with a stock '08, experience detonation under a bad set of circumstances involving fuel quality, temperature, and operating conditions, it's safe to say that the same thing can happen to your '13. So if the bike happened to be on the edge of knocking at 3/8 throttle @ 6500, and you dial in a +2, it may very well cause knocking, and knocking is always a problem. However, on the whole, adding advance with the tuner is a reasonably safe thing to do.
In the most general context possible, adding advance will usually increase power, retarding will usually "soften" it.
Fuel ratio is a different thing. The first thing to know about it here is that 4-strokes are enormously tolerant of less than optimal air/fuel ratios, vastly more so than two-strokes. You can set up a condition in which there's a lot of advance and a very lean mixture and cause detonation problems that way, but in most cases, before they get lean enough to hurt themselves, they start running unacceptably bad, so it doesn't happen often.
The second thing, in light of the video, is that the ideal, stoichiometric ratio of 14.7:1 is only ideal in chemistry. You get more fuel efficiency at slightly leaner (more air) mixtures, and more power at significantly richer mixtures. The best power output is normally at ratios around 13.5 - 13.8:1 somewhere, and that will vary according to fuel chemistry and environment. An engine that is a little rich at a mid RPM/part throttle condition may cruise a little dirtier, but will seem sharp and responsive when called upon. Too rich, and it will blubber and stumble before catching on.
Again speaking generally, a leaner engine will produce less power and feel less responsive and "sharp" than a richer one does, but at the same time, very rich engines have a tendency to get rough and grumpy, and are prone to stalling when they idle down fast. How adding fuel or subtracting it affects your bike will depend on how relatively rich or lean it already is in the cell you're changing with the tuner.
As mentioned, the tuner doesn't make large scale changes that would be likely to cause problems. It may be possible at the extremes under certain conditions, but on balance, you don't need to worry too much about it. I'm just guessing, but I would say that it can move ignition timing perhaps 2-3 degrees in either direction, and change the fuel the equivalent of 2-3 jet sizes up or down. Also note that at least one TT'er has found that his bike runs better by reducing fuel pretty much across the map, so you kind of have to try one thing at a time, see the affect, and adjust.