What kind of evidence supports the belief that molecules of various kinds, exist in space?
It depends on what you mean by space. In orbit around earth, satellites have sampled the vaccuum and have been able to directly detect the molecules. Additionally, the gradual slowing from friction caused by these molecules is the reason that satellites occasionally need to be ‘reboosted’. In interstellar space or interglactic space, these molecules are detectable using spectrographic or radio methods. Variations in the amount of light coming from distant stars can show clouds of molecules on the path between the earth and starts (nebula). Standard statistical models of molecular motion show that there must be some distribution of molecules in vaccuum. If there are some molecules somewhere, they will gradually become evenly distributed.