If by other faiths you mean non-Christian religions that is true. They are not sacramental but they are natural and valid.
No, the Church does not recognise the second marriage. If two people have no religion and marry in a civil marriage ceremony their marriage is valid. A civil dissolution of marriage, commonly known as divorce, does not end that marriage. They are not free to re-marry.
You cannot really be an ex-Catholic. I know there was a period of time when one could formally defect but that is no longer an option. A lapsed Catholic is one who does not observe the Church’s precepts but is still a Catholic. An excommunicated Catholic is still a Catholic and excommunication is a medicinal penalty with which it is hoped they will return to the faith. Therefore, they are different from your atheist example. They would marry for life and civil divorce could not end their marriage. They would also be bound by canonical form. If your hypothetical situation were possible and you could truly become a non-Catholic you cannot reverse baptism. So their marriage would still be a sacrament and civil divorce cannot dissolve the sacred bond of marriage.
In the same way it evaluates the marriages of Catholics. They only thing it would not hold them to is canonical form. Everyone, Catholic, non-Catholic Christian, non-Christian and non-believer are still bound by natural and divine law.
Like anyone else they would be living in a state of public sin. Non-Catholics are not bound to canonical form but must marry in some form of acknowledged marriage ceremony and this could be a civil ceremony or a Protestant, Jewish, etc. ceremony. You cannot simply share a house and a bed and say that makes us married.