Hello community!
I've got this bonsai tree in november from my mother. I don't know its species(maybe you can also help me identify it). When I moved it to my home- approx 300 kilometers away- it dropped all of its leaves in 3 days. Ever since it just grows these green sprouts. First i cut all of those, after a while i read about it that I only need to cut the top of those sprouts I always left 3 leaves I thought it will make it grow thicker. But then those leaves i left on it started to writher and die. I was worried it will not start to grow the sprouts again. But it did and now its back to point zero. I give it ?broth regularly and its pot is always somewhat semi-wet, but not soaked. Its in a sunny place- my flat is on the southern side so the room its in is in sunlight constanly. I'm thinking abut cuttin all the little branches, to make the tree regrow them I'am afraid that it will kill it off completely. I never had a bonsai before (obviously) and i really like to save it, however long it takes.
Any advice will be appreciated. Thank you!

Looks like a chineese Elm. It needs to be outside to survive.

Is there a hole in that pot?

If this is the place where you keep it, it is sitting too dark

yes,there are holes at the bottom there are four holes plugged with soft polyester(probably) but it leaked a bit onto my table so i put this plate under it.

Open the holes completely and, like LB said it needs more light, preferably outside if it's not freezing where you live

Although the picture is quite dark, i think this is a Chinese Elm indeed.
If you have put it in the south facing window, and you are sure that it gets quite some hours of full sunlight, this isn't your main problem.
I've got a Chinese Elm in my south facing window, and it gets full sunlight for almost the entire day. Also, it's growing like crazy.

I assume the problem is somewhere else. First of all, I would stop cutting parts of your tree unless you have some clear aesthetic reasons. In my opinion, cutting will only increase the stress on your tree. So don't do it when you think your tree is dying, it won't make it easier for the tree to recover.

Pruning back a Chinese Elm to 2-4 leave per shoot is good, however don't do it too rapidly. Wait for a shoot to become rigid before you prune it. Also take into account some die back. So if you cut the shoot, it will die back up to 5-10mm. If you cut too close to a leave, this leave will then die back as well.

Finally, make sure you don't over water it. For me, once the top layer of the soil starts drying out, I will insert a wooden chopstick or wooden toothpick in the soil and leave it there for aprox. 10 min. By doing this you can check the humidity at the lower layers of soil. Also ensure that the soil and the pot allow good drainage of water.

Good luck!