So I want to make an obsidian farm. Unfortunately I have only 1 bucket of lava. Now the question is is it possible to make any obsidian farm on the earth surface or are there any rules stating otherwise?
Yep, minecraft doesn't really check if you're on the surface or not for making obsidian, so any farms that work underground will also work overground.
There's a farm design that only needs one bucket of lava which is not consumed. You will be able to get 1 obsidian for every 1 redstone dust you have.
Here's a gif I made if you want to know how to make/use the farm: http://img821.imageshack.us/img821/4127/h0q.gif
Here's the minecraft wiki page on obsidian farming: https://minecraft.wiki/w/Tutorials/Obsidian_farming
Here's also a video tutorial (Not mine) showing the same thing:
The only way you can make obsidian on the surface is to find a surface lava pool or move lava from the Nether/cave and put it down on the surface (and then turn it into obsidian in the normal way)
You can't 'farm' obsidian in the way you can farm wheat/melon etc. - you can only have as much obsidian as you have lava.
Edit - there is a way of mining infinite obsidian using redstone.