1. God is so busy in taking care of the business of the whole world and in order to save his time and efforts, I don’t want to trouble Him with my personal affairs and trifles;
First of all, we as God's creation wouldn't be able to live without the constant care of our Creator, God our Lord. This is in some sense very similar to the dependency of computers on their creator, the human kind. No matter how superior a computer is in its own way, it wouldn't be able to function properly or even survive without the care (i.e., maintenance) of mankind, its creator.
Secondly, God is willing to take care of us and therefore every business of our lives because God is love. He cares about us because He loves us.
Thirdly, God is capable of taking care of everyone's every business. Just as the scripture says, even our hairs are numbered by the Lord.
Last and not the least, as pointed out by Albert, God wants to involve in our lives because He wants us to fulfill His objective of creation, i.e., glorifying His name.
In conclusion, God is capable and willing to take care of our business and has actually always been doing so. What we need to do is to acknowledge that and willingly seek His guidance and care in very trial and trifle of our lives.
2. Since God had destroyed and cleansed the fallen world once with the great flood in Noah’ time, and since the world has once again become filled with sins and evils, why couldn’t God destroy and cleanse the world once again by some method but chose to send his son to the world?
God did not destroy the world but judged the world using the flood. One primary purpose of the judgement of flood was to make clear to the mankind in a spectacular way that the consequence of sin is death. Knowing the salary of sin is death is the essential first step for sinners to repent and therefore be saved.
The salvation of Noah's family through the flood also signifies the salvation of baptism with water. As Jesus the Lord points out, sinners cannot enter the kingdom of God unless being reborn through water and the Spirit.
In other words, the judgement of flood was part of God's salvation, which was ultimately fulfilled by the incarnation, death, and resurrection of His only begotten Son, Jesus Christ our Lord.
