What would change if our earth lacks mountains?
Well, mountains are not a cause. Mountains are an effect. It's not that we have earthquakes because we have mountains. We have mountains because we have earthquakes.


  Earth as we know but without mountains (mountains have never been formed or don't exist at all)


So by saying that mountains never existed at all, you are implying there are no tectonics. That would be a sad thing - one of the things that make Earth so alive and interesting is the fact that we have plate tectonics. Go and have a look on Mars, the Moon, etc. There are no active tectonics there are those are dead places.


  What will happen if the Mountains would just been taken away?


They would just form again. First of all, there would be the effect of isostatic rebound. When you take away a certain mass from an elastic thing, that thing bounces back up. When you're sleeping on your bed, there is a dent in it. When you get up, it springs right up. This will happen also in the Earth. It is happening actually as we speak - certain places in the world (Scandinavia is one example) that are slowly rising because the huge ice sheets that existed during the last ice age melted. That said, India is still colliding into Asia and the Mediterranean is still closing so you would get more Himalayas and Alps. Plates are still subducting so you you will get volcanic arcs such as the Andes or Japan. It will take some time, but the mountains will come back.