Eden - The atmosphere of the earth 4 billion years ago contained no oxygen therefore the composition of the oceans was also quite different. Modern vents are also teeming with existing lifeforms.
Life will not likely arise a second time on earth. However each of the steps to life is being investigated in labs all over the world.
For almost 2 billion years there were only morphologically simple pokaryotes. If life is discovered on other planets it will probably be bacterial.