1) Where are other ships and what happened to them?
The movie does not provide us with the answer as to what happens to the other ships.
At this point we can do nothing but to speculate all those whats and whys.
Of course you don't clutter all those giant ships at one place. They are spread across the universe (well within permissible distance). Those were not shown probably as the story can run independently without any necessary inputs from them.
2) Why does only one ship provide operations with EVE on Earth?
We see Buy-N-Large has the monopoly of overseeing the welfare of people and the society. They have the power of governance in the spacecraft and we can assume that they had are in control of other spaceships too. So, when one unit of them is sending EVE to check the status of earth, the other units refrain themselves from wasting their work power.
Also there is another possibility. Others may have sent other EVEs in other parts of the earth, but they didn't end up with the interesting events as EVE does, so we don't need them in the story.