But when there was no human, but some single cells, How do you classify them?
In other groups. The living world contains a lot more than just plants, juvenissun. If an alge is not a plant (single celled), and not an animal (animals do not have cells with a cell wall), it is something else. It gets its own group.
Depends on the organism. If it doesn't fit into any of the groups we have, it gets it's own.
Don't we say they are animals in contrast to plants (single cells too)?
Not necessarily, some single-celled organisms are animals, but not all single celled organisms are animals.
We do not even say that they are cells, because there was nothing else around. Single cell was the only life form at that time.
And?
Imagine that NASA discovered some cell fossils on Mars, what would be your first question? Would it be: what kind?
Sure. But if it is unlike any kind we know, it just gets its own. When we discovered a group of single celled organisms that looked like prokaryotes but weren't, they got their own name also. Archaea. They got their own group, because they weren't eukaryotes, but weren't prokaryotes either. And those were the only two overarching groups we had. If it doesn't belong in either of them, this means that there is a third group.
If we discover a fossil cell on Mars and it is not an archaea, not a prokaryote and not a eukaryote. I'd like extraterrestria, but if anyone has a good suggestion I'm all ears.
To fit theology into the discussion, my definition of plant is: cell or cells made of non-animal cells. Comment?
Why would we want to fit theology in the discussion. I can't think of a more useless exercise. There are more things on this earth than plants or animals. If the jews writing Genesis weren't aware of this, tough for them. Luckily, we've come a long way forward in our knowledge of the world since then.