My female cousin got married and I know for sure that her father wasn't present during that process because they don't talk to each other. Am I obliged to advise my cousin that her marriage might be invalid while I know that she isn't really practicing and probably doesn't care what I have to say?

Ustadh AbdulAziz al-Haqqan

It seems like you are not even sure of the details, how can you then nullify a whole marriage? If her father let someone else do it on his behalf it is valid.