Your question is really many questions in one! Basically the keys to good turf care are mowing as often as possible, watering deeply but not any more often than necessary, fertilizing with a 3-1-2 product at a rate of 1 pound of nitrogen in mid spring, and again in early to mid fall, and doing whatever tree triming is needed to brighten the area as much as you can.
In order to provide a more thorough answer than can be put in this small space, I will refer you to the following Internet sites. They will provide a wealth of information for you.
Thanks for the question. Please stop in again soon!
Q&A Library Searching Tips