There is a very basic difference between all life on Earth and the type of life you are suggesting.
Look at the image below.
This is a simplified image of a DNA double helix found in cells of Earthly life.
When a cell divides into two (mitosis), the DNA string divides into two strands and each strand is then joined in by a matching strand so that two sets of DNA are formed.
In your world, you want a cell to divide into not 2, but 3 children cells. This would require not a double but triple helix structure, so that each child cell inherits one part of it and completes it. Something like this:
Now lets refer to your questions.
1- How would life (both unicelluar and multicelluar, microscopic and macroscopic) be different from life on Earth? What advantages and disadvantages would this sort of celluar division have when compared to normal cell "duplication"? Would completely "alien" lifeforms evolve?
For one, that life would be very different from the life forms we know of, at least on cellular level. The whole method of protein coding would be different from Earthly life forms. We don't know different it would be on macroscopic level.
2- What would be the reason for such a development?
Because you want it to be like that.
Or the spaghetti monster ordered that.
Or the cells got bored of mitosis/meiosis one morning and get apeshit insane.
Or a super wizard cast a magic spell on those cells.
3- How would growth be different? Would this sort of cellular division mean that the amounts of biomass can increase more quickly?
We have no idea how growth would be different. Cell growth and cell reproduction are completely different things.
No, this sort of cell division does not necessarily mean that the amount of biomass can increase more quickly. For example, in favorable conditions on Earth, a bacterium undergoes mitosis in about 20 minutes. If a bacterium undergoes this type of triple cell division and one cell takes 40 minutes to divide then that those organisms would proliferate slower than organisms on Earth.
4- Would ecosystems be different?
You are confusing cell division with ecology here. Although these subjects might be related on some higher-than-human level of understanding, at this time the best and brightest minds don't know what would/could be the direct impact of this type of cell division on the ecology of a habitat.
5- What would happen if an organism from this planet would be exposed to the Terran ecosystem?
That organism would feel very lonely and nostalgic. Nobody would make friends with him and he/it would cry in a dark, secluded corner.
OK enough sarcasm. Here again you are mixing cell division with ecosystem. The possibilities are endless. Maybe it would go on living happily on Earth and call it a new home. Maybe the oxygenated environment would be toxic for it (nothing to do with cell division mechanism btw) and it would die.
In short, you are asking a question like => if all gray monkeys were blue, would they choose to twerk with Scarlett Johanson or Condolisa Rice?
I am not a blue monkey so I can't say for them, but I would definitely choose Scarlett Johanson any day!