Rusty,
To address your knowledge gaps (even though the job is now done, it never hurts to understand 'why' they are necessary.....
1) There is no such thing as 'brake disc warp' (in the sense that most people would understand as 'warp') - if you think about it, the discs are fairly chunky bits of steel, and to get enough heat into that volume of metal to warp it would mean driving through Hell itself (or I suppose, an errupting volcano may do it.....) - either way, by the time that happened, the car would likely be destroyed anyway by radiated heat!
That's not to say that the discs aren't affected by the heat from brake applications.....
..... the material structure of the mating surface between disc/pad change with heat application.
The easiest way to understand it is to consider playing with sand on the beach - I'm sure we've all (at some stage) built a sandcastle, and the first step to any sandcastle is to make a perfectly flat base.... usually achieved by scraping a spade (or an arm) across a patch of sand until its smooth and flat - this is your brake disc.
Then, if you again wipe your arm across the dry sand, but press down very slightly, you will 'plough' a small quantity of sand particles in front of your arm - but when you stop, most of the accumulated pile of dry sand will spread out across the imediate area, but a small quantity will remain proud of the 'flat bit', as a ridge..... (your arm is the brake pad!!).
Back to the car..... As you apply the brakes, motion energy is converted to heat energy in accordance with the laws of Physics, as the brak discs heat up, the metal particles change density within the structure, and some will move arround the disc as it rotates (pile of sand), when you stop braking, the heat dissipates, and the metal stabilises (but the density still varies due to the movement of particles).
The only way to prevent it (with 'modern' brake pads anyway!) is to ensure that you only brake for as long as it takes for an EXACT rotation of the disc (or multiples therof), and get the same temperature into the entire disc, and when you stop braking, imediately cool the disc down to ambient temperature evenly, oh, and change the pads after each braking incident.....
...so it can't be done....
obviosly, we are talking atomic levels of distortion, and it takes a while to happen, so goes mainly unnoticed until it gets too bad.
If you then get your disc skimmed, it will return to 'flat' but the material density is still disturbed, so wear will never be even, and the same thing will start all over again, but each time it's skimmed, the rate of wear will increase.
This is why i change my discs every time i change my pads (but I suffer OCD on braking issues!).
If you think what would happen if the disc was made of plasticine, it would be simple to visualise, and the wear (and material distortion) would be immediately obvious

.
2) "Run out" refers to the disc running in the same plain as the hub - it needs to have flat mating surfaces, free of loose rust, particles and paint. If the 2 items don't mate correctly, then the disc will not run 'straight', causing one area to touch the pads before the opposite side - it can be accurately measured with a dial guage, but is usually obvious when you refit the wheel and rotate it - you may hear one bit touching before another bit as the wheel turns.
3) New pads/discs need a while to 'bed in' - ie, the pads and discs will wear against each other until it gets to the stage where the entire pad area is in contact with the rotating disc...
...this is compounded with the brake pad material construction - it's a bit like the material construction of the disc, but far more 'granular'. Heat affects the density of the granules.....
....as such, all manufacturers will publish 'bedding in' details for each brake compound they supply - for example, on Ferrodo DS2500, you need to drive at 40mph, apply the brakes firmly (in a straight line), until you get to 5mph - repeat 3 times - do it again at 70mph - all done! this allows the material to settle down - the solvents used in the manufacture will heat up and dissipate, and braking will be okay.
With new pads,this effect is compounded by possible oil contamination on your fingers, or protective grease on the new disc...
.... people tend to worry about grease/oil on the brakes more that you should - obviously there will be a negative effect on braking performance, but it would have to be an awfull lot of very slippery grease before it makes a huge difference.