Mary and Elizabeth were certainly relatives. If one relative went to visit anther relative a long way off and stay for three months, that would indicate a close relative like a first cousin or a niece/aunt relationship. Hence most assume they were first cousins. It seems that Mary came to be of assistance to Elizabeth during her last three months of pregnancy.
The Pope is only infallible under very specific circumstances if one reads the CCC carefully (and it must be read carefully, especially by people who understand such documents). He can’t be said to be infallible because that means that any statement he may make or anything he writes at all are infallible and this has never been the case.
