EDIT: Cardinal Ape beat me to it.
Each full turn that a Corps is attached to an Army (i.e. not the turn you attach it) the Army commander makes a roll to see how much (if any) benefit he will provide to his subordinate Corps commanders. The better his stats, the more likely he will pass a benefit to his commanders, and the higher it is likely to be. (Poor Army commanders CAN pass negative ratings if they have low stats.)
To find out whether and how much a corps is receiving, select the corps stack and look in the bottom right. Above the supply ZOC, etc, there will be a tiny silver diamond marking that this is a corps. Hover over it and a tooltip will pop up telling you what benefit he has received.
These benefits apply to the corp commanders stats. So if it says he receives 1 to his STRAT rating, then that is what he gets, and his ratings when you hover over the commander reflect this bonus.
1) No, it is usually 0, 1 or sometimes 2 in the case of Lee or Grant. -1 is not uncommon in the case of early Union 3 stars, I can't recall having ever seen a -2.
2) This doesn't affect the calculation, only the Army commander matters. (AFAIK.)
3) This is a vague line in the manual that you can mostly just ignore because it is so handwavy and over-simplified that it is meaningless. Most importantly the STRAT rating affects the activity/inactivity roll and a commander's ability to withdraw from a battle if necessary. It also increases the frontage available to his side if it is very high, like a 5 or 6, but that may only be if he is an Army commander and his stack is actually fighting, I can't recall for sure. It affects a couple of other minor things that are not that big of a deal. However increasing the STRAT rating is extremely important so that the subordinate corps can be active more often, dramatically affecting the ability of an Army to function effectively. 3 STRAT commanders are inactive around half the time, 4 STRAT only around a third of the time (it's more complicated than that, but is a good rule of thumb).
The OFF and DEF numbers can in certain cases give all of the Corps commanders and the troops fighting under them +5% to their base chance to hit for each point the rating outnumbers the enemy's opposing rating. This is +5% of the chance to hit, not +5% to the chance to hit (i.e. *1.05, not +.05. If the base chance to hit is 15% you would be at 15.75% not 20%). This is 5% for each full point comparative advantage of the stack commander, the unit commander gives a corresponding 3% bonus but they are not affected by the Army/Corps bonus system. If the enemy still outclasses your combined OFF/DEF ratings you get zero bonus to-hit no matter how good you are and the enemy gets a bonus based on how much better he is than you.