Is Each Breathe We Take the Grace of God?

Yes.

Ps. 104:29 "You take away their breadth, they die and return to their dust."

Does God Leave the Earth to Run on Its Own After Creating It?

No. He continues to sustains it. Provides for it.

Ps 104:14 "He causes the grass to grow for the cattle and vegetation for the service of man that it may bring forth food,"
104:19 "He appointed the moon for seasons, the sun knows its going down,"
104:21 "The young lions roar after their prey, and seek their food from God."

How Should We Respond When Our Enemy Falls?

Pr 24:17 "Do not rejoice when your enemy falls, and do not let your heart be glad when he stumbles."

We should not gloat the failure of an enemy for that displeases God. In fact, God will discipline us when we do so.

Pr. 24:18 "Lest the Lord see it and it displeases Him, and He turn away His wrath from Him."

Is God Evil When He instructed the Israelites to Completely Destroy their Enemies when entering Canaan?

Actually, such a question is already disrespectful to God as we are not trusting in His sovereignty. But the bible also clearly tells us the reason why He does so.

Deut 7:4 "for they will turn your sons away from following me to serve other gods, and the Lord's anger will burn against you and will quickly destroy you."

If the Israelites did not destroy them completely, they would intermarry with the pagans and be influenced to idolatry and all other kinds of immorality associated with it.

One debatable point which others have also raised is that by killing those who have not reached the age of accountability, God is actually merciful to them by ending their lives prematurely before they are allowed to fall into sin.

What should we beware of when we seek to obey God's commands?

We should not fall into the trap where we outwardly obey the commands of God but yet in our hearts, its actually willful disobedience.

Deut 5:29 "Oh, that their hearts would be inclined to fear me and keep all my commands always, so that it might go well with them and their children forever."

With outward actions, we obey. More importantly, we obey in reverent fear to God in our hearts. We do this because He is God. And a added bonus is, He blesses us when we do so.

Are there other gods other than the one revealed in the bible?

No.

Deut 4:39 says "Acknowledge and take to heart this day that the Lord is God in Heaven above and on the earth below. THERE IS NO OTHER."

Deut 5:7, in the first of the ten commandments, "You shall have no other gods before me."

We don't have to waste time looking for false gods in our lives. The one true God, creator of the universe, of this world, of the lands, of the seas, and of you and me is revealed in the bible. Pick it up. Read it. Obey it. You will know this God. I can't describe the blessings that will be poured upon you if you do so.

How do false teachers deceive people?

False teachers are not obvious. Hence, only then are they able to deceive people as they are mistaken as true teachers. So how do they do it? They do not go around saying that Jesus is false. Such are blatantly obvious. What they do are secretly, subtlety, they infuse twists and turns into the Word of God.

Deut 4:2 says, "Do not add to what I command you and do not subtract from it, but keep the commands of the Lord your God that I give you."

False teachers slowly but surely add extra man made stuff into the bible. They will say, you should pray in detail what you want for, only then will God know what you want and thus will provide. If you are not detailed enough, your prayers will not be answered. One proponent of this is Cho Yonggi, mentor of Kong Hee.

Another way that false teachers tweak the bible to fit the interests of man is to subtract from it. They preach that God will cause prosperity. But they do not preach that He casts down woes as well. They preach that God will give. But they do not preach that He takes as well (Job 1:21). They preach that God saves, but they do not preach that God judges as well. One such proponent is Joel Osteen.

We should take the whole counsel of God. Not add to it man centered ideas, nor take away the works of God which we do not like to hear.