Pokemon Stats Breakdown

You can generally find all the information you're asking for at Bulbapedia.

For example, here's the exact damage formula.

Speed directly dictates who goes first; it's only random in case of a tied speed stat.

Natures always increase one stat by 10% and decrease another stat by 10%, or have no effect.

Additional answers:

1. Base stats are simply used in the formula for determining current stats. They don't necessarily correspond to stats at any level at all; they are just numbers that are meaningful relative to each other.
2. I prefer Psypokes. For each Pokemon, you can change to see their stats, levelup moves, TMs, etc. for any generation where they existed.
3. Bulbapedia has a list of all moves, sorted by generation in which they were introduced.
4. Psypokes will show you moves by level, but for stats you will have to use some formulas from Bulbapedia.