As far as I know it is used in all parts of the English speaking world, you can find the exact history of it here http://www.worldwidewords.org/qa/qa-pin1.htm As the Dutch word for this finger is "pink" it likely first came to Scotland, then slowly introduced into the entire English world. There is also the "fore" finger *the one you point with and the "middle" finger".

I have never heard of another name of that type. It is usually known as the "little finger," rather than the "small finger," though.

We also say ring finger for our fourth finger so really every finger has a name of some sort. Interesting that it might have come from Dutch!