Dear Christina:

First a little background:

The Sacrament of Marriage, by virtue of being a Sacrament, is a holy estate that is not to be taken lightly. The purpose of marriage is briefly explained in paragraph 2363 of the Catechism, though the Catechism discusses all aspects of marriage more throughly in the rest of this section and 1601ff.

The spouses' union achieves the twofold end of marriage: the good of the spouses themselves (the unitive) and the transmission of life (the procreative). These two meanings or values of marriage cannot be separated without altering the couple's spiritual life and compromising the goods of marriage and the future of the family.

To get married for any other reason than to have and raise a family (if the spouses are both fertile) is inappropriate and disordered. Marriage merely for financial arrangement or for mere companionship between two fertile persons violates the virtue and sanctity of marriage.

In addition, "The conjugal love of man and woman thus stands under the twofold obligation of fidelity and fecundity... Sexuality is ordered to the conjugal love of man and woman. In marriage the physical intimacy of the spouses becomes a sign and pledge of spiritual communion.

Marriage must be consummated. If either the man or woman is permanently impotent, that is, incapable of having intercourse, then the couple cannot be married validly. The impotence much be complete and permanent.

If the couple can physically have intercourse, but one or the other is infertile, the couple may still be married validly since the first end of marriage, "the good of the spouses themselves," (unitive end) still applies even if the couple cannot have children.

A couple who is capable of having children, but intends on never having children, may not a be married validly.

A couple should not abstain from the marital embrace except for brief times, such as for a spiritual exercise, or the practice of Natural Family Planning when NFP is allowable.

If a couple mostly abstains both the unitive and the procreative end of marriage cannot be realized. For infertile couples the marital embrace is still very important as it is the mutual self-giving of the spouses to each other in love. This bonds the couple in a profound way.

As for your questions:

Is it sinful for a person of the Catholic faith to marry outside the Catholic Church with someone of another faith?

Yes. A Catholic must be married in the Catholic Church, even if that Catholic is marrying a non-Catholic. For a Catholic, any marriage outside the Church is invalid, which means that such a Catholic is in a state of sin and cannot receive the Sacraments, since to have sex without a valid marriage is the sin of fornication. This point, of course, is presuming the couple are having sex, which is to be expected of a married couple.

If the married couple, live as brother and sister, or live apart, never having sex, then the Catholic spouse may receive the Sacraments since fornication is not committed. The invalid marriage itself is a sin, but it is a singular sin in time, which can be forgiven in Confession. It is having sex repeatedly that perpetuates the sin of fornication that bars one from Communion. 

But, to purposely get married outside the Church for financial gain with no intention of really being husband and wife, is not only an act of sin and it does violence to the dignity of marriage. It is an abuse of God's gift of marriage, which means that it would be an abuse of God.

In any event I fail to understand why a couple needs to be married only for financial reasons, living apart, with no intention of living truly as husband and wife. There is no reason to do this. A financial agreement between the couple can be made without having to be married. I cannot think of any issue of finances that cannot be accomplished by contract, trusts, gifts, investments, or other financial instruments or agreements or sharing of expenses.

There is really no reason to sin or to get married at all in this scenario. Just make whatever financial arrangements the couple wants for each other through contracts and the like. Marriage is not needed.

Is it a sin for an older couple to live together - under the same roof but without any sexual relations as both are not married, but living together purely for companionship and financial benefit.

No. There is no sin in a housemate arrangement, even for young adults, as long as the couple does not have sex.

Such an arrangement, however, requires wisdom, prudence, and self-control. The couple needs to be especially watchful for situations that place them in the "near occasion of sin."

The near occasion of sin is not sin, but means that one is getting too close to the fire and thus may get burnt. Never underestimate one's own weakness. We are not has strong as we think we are. 

For example, if living as platonic housemates, the couple should relate to each other in the same way as they would with a roommate who is a stranger. That means modesty — not parading around in one's underwear, ensuring privacy of the bathroom, no sleeping in the same bed, or anything else that would unduly place the couple at risk for falling into sin.

But, if the couple are careful and behaves with modesty and proper decorum as they would with any roommate, then this arrangement can successfully meet your scenario without sin.

 I hope this helps.

God Bless,
Bro. Ignatius Mary