dawid2991

saw that thing, and it is an ugly as hell thatch building

From what i managed to observe, the character (don't know about the tames) gets less debuffs from temperature in an enclosed room. So maybe you should try to enclose a breeding space and check if this helps. But thats just my speculation

The wild Turnip is not the taming food, you need to plant the seeds that you get from the wild turnip and grow normal Turnip, which is the taming food for rhinos. That is probably the reason why your taming went so slow.