Karzai was elected fairly the first time, and the second time he would have been elected even without the fraud (the fact that he organised fraud shows how stupid he is) - given that he has dealings with the taliban, various warlords and pakistan, if he is our puppet then we are incredibly stupid for not picking someone who will actually listen to what we want.
Secondly we dont murder civilians openly nor wantonly. If this was the case you would see corpses hanging outside of towns as warnings to others. The fact that the US army/airforce desperately tries to hide any civilian deaths tells you everything you need to know about what they think of openly murdering civilians. The fact that troops bitterly hate the rules of engagement which they say puts their lives in danger all to prevent civilian causalities shows its not done wantonly.
Thirdly the US is not actually hated around the world. Why people believe this I dont know. And for that matter, for all the hatred of the US in the middle east, you only need to check the lines outside of the US consulates to see what people really think.