So it's like earthfag, airfag, waterfag and firefag in the US

And we should not forget the new metalfags in legend of korra

Metalbenders are just specially trained Earthbenders though. Plus Toph could do it in the original show, so they aren't even "new"

Indeed. In the original series I remember swamp benders being mentioned(I haven't seen all the episodes though). Swamp bending is the combination of Earth and water bending.

And there's also Bloodbenders,
but they're just waterbenders too, they just bend the water that's inside the blood of a living being

No. No it is not. That's impossible. Only the Avatar has more than one bending power. Swampbending is bending the WATER inside of plants. Swamp Bending.

Similarly, Sandbending is the bending of the individual grains of EARTH (well, Silicon DiOxide) which make up sand. Sand Bending.

No offense, but seriously:

1. Any amount of Avatar knowledge should really yield "no one but the Avatar can bend more than one element."

2. Either Toph or Katara proved themselves to be able to bend that on their own, wince it's a mixture of water and earth, the other half of the solution is carried with the part that is bended.

3. That wasn't even similar to what the Swampbenders did. That was mud (silt, but the basic composition), Swampbenders bend plants.

You sir are correct. I secede due to my failed memory and lack of knowledge on the subject. I just re-watched the part I was referencing. Katara and Toph were indeed both able to bend the slurry independently. They combined their abilities to make clogging the waste more efficient. I remembered Katara saying something about swamp bending at that time, but my memory was flawed.