I agree with Cody, you can go in a smash stuff for a while, but eventually it will stop working. This can be for various reasons: overreaching, too much volume, too little, etc et c.
I think your second question is the most interesting, as it really depends on the type of routine you are following. If you have a specific meet/testing day in mind and want to show up at your absolute best on THAT day, then I think going off program is very counterproductive. The entire program is centered on making you ready for that day; by deviating from it, especially going heavier than you need to, you are defeating the purpose of programming. Now, if you aren't training for a specific event, you can just sort of wing it and hit PR's as you can, but I think it tends to only work for a short period of time before stagnation.
Number 3 I think has an easy answer; do the bare minimum to garner results. If you are already so trashed that you need to rest forever and a day and use lighter weights, you are done. Think of it this way, if you do too much or too little, either way you are not at your best. If you are going give up a few lbs to your best, wouldn't you rather train less, not more? You will feel better, be more recovered, and likely have improved motivation since you are killing yourself every time you step in the gym.
Axle Press (270x4), Log Press (255x1), Farmer's (215/hand, 50 ft), Strict Press (225x1