It's not fully explained as how Edward is able to use alchemy by just using his hands.
'The Truth' that he has seen after he tried to resurrect his mother is the key to how he performs alchemy with only his hands. Before, he can just dry a circle on the ground.
The exchanging of elements is what alchemy is made and composed of. In one of the episodes where Scar comes in, Armstrong mentioned 3 processes: decomposition, restoration, and creation.
Edward's use of alchemy is basically combining or breaking the elements. You have to know what you're doing or you'll screw up. Basically, looking at the scientific chart, let's say Ed can try to make water or decompose it. Water is a mixture of oxygen and hitrogen. By breaking it up, Edward can just clap his hands to break or separate the elements without exchanging anything. There's a counter balance used for this.
When Ed creates a spear, there's basically a hole in the ground leftover. Looking at the spear, it's made of the ground's rocks and metals.
The hand thing that you mention are made from the materials of the house. There's no exchange as long as there's equal amount of material to use at your own expense. Ed used that 'hand' fast enough to save the cat or he would have destroyed the house.