Which genes do not code for proteins?

Those would be the non-coding RNAs. These are genes that are transcribed into RNA, but it will stay as RNA and wont make proteins. 

Examples: 

transfer RNA (tRNA), ribosomal RNA (riRNA), small RNAs (snoRNAs), siRNAs (silencing RNAs), etc. They have functions, but as RNA, not as proteins. 

Hope it helps!! 

mostly all of the genes code proteins but eukaryotic DNA has a repeated sequence that  doesn't encode for proteins.

It might. it might because if you think about if they discovered if we came from (lets say something funny like aliens) and thy found cells that matched and they would have t do more research about it but would most probably change their theory.