Parents, first and foremost, it is important to... understand and recognise the activities your child is naturally gravitating towards. It's important also to ensure that your child likes what he or she is doing. I believe in exposing children to as many hobbies and extracurricular activities as possible.
It's important, according to me, to train in small doses so as to not lose the joy of playing chess. I personally think too many coaching and training classes may take away a child's interest in the game itself. The essential thing to do is practise often and, in case of a doubt, to consult a trainer.
Grandmasters decline with age. That's a given. There is nothing special about the age of 40, but age eventually takes its toll. That much is clear. Beyond that, it's about how long you can put off the effects and compensate for them. Mistakes will crop in, but you try to compensate for them with experience and hard work.
I think an important lesson from the game is that once you have made a move, you cannot take it back. You really have to measure your decisions. You think a lot. You evaluate your choices very carefully. There's never any guarantee about what's going to follow once you have made a decision.
Before a game, I avoid having a heavy meal so that I don't feel sleepy at the board. You eat to be healthy, and that generally takes care of everything. Also, you can't be too finicky, since at tournaments you tend to eat at restaurants here and there. But, as long as you're eating sensibly, it's all good.
The broader the chess player you are, the easier it is to be competitive, and the same seems to be true of mathematics - if you can find links between different branches of mathematics, it can help you resolve problems. In both mathematics and chess, you study existing theory and use that to go forward.