Why was Abe sent from the future and where is Abe in the present?

It is not mentioned how the time-travel works in Looper. You seem to enter a chamber to 'depart' but when you arrive you don't need any sort of equipment. It may be that time travel only works 'one way' that you can only go into the past. There is talk of 'news' from the future - which implies that messages can be sent back (physically at least).

So when time-travel is invented I think we are meant to presume that the gang leaders in the future think this is a great way to dispose of bodies - BUT they need some sort of reliable way to ensure that the people are killed and the bodies disposed of.

There are all sorts of potential plot holes here - like why not send them into a volcano, or into water or whatever. Ignoring these issues, if you decided that you need some way to set up the network of loopers, show them how its going to work etc - then you need a manager to go back and set it up. You reward him by setting him up in his own fiefdom in the past, send him silver/gold etc - or let him bet on baseball results ala Back to the Future.

So my answer to 1 is .... somewhere in the present, doesn't really matter - but he is there to set the looper system up in the first place. He is the bootstrap.

Who ordered him. Its not clear whether the Rainmaker is his boss, or whether he works for another crime organization. I don't think this is clear.

1. Abe was sent from the future to manage the Loopers. As for present-Abe, this character may not even have existed yet in the movie's time setting (2044). Maybe Abe was born in, let's say, 2049 and was sent way back in the past to, let's say, 2025. So for 19 years up to the movie's time setting (2025 when he was sent from the future to 2044), Abe was already working to manage the Loopers. There is even a scene where Abe explains how he first met Joe.

2. Probably the crime lords from the future who used time travel to dispose the the future crime lords enemies.

As for the Rainmaker, his ascent to power is aided by his telekenesis. The last sequence explains how Future Joe causes a young Rainmaker to become vengeful and destroy the loopers from the future (2074).