Is it forbidden for one to enter into a "misyaar" marriage with a woman who is older than him and belongs to a heretical sect, even with the presence of witnesses and a symbolic dowry, and if she shares in the living expenses?

It is fine for the wife to be older than the husband, but the marriage may be flawed by other matters:

1. The woman adhering to an innovated (bid'ah) doctrine: If the innovation is disbelieving (mukaffirah), then marriage to her is not valid. If it is not disbelieving, then the marriage is valid, but refraining from it is preferable, except with the intention of saving her.

2. Completing the marriage without a guardian (wali): This is invalid according to the majority of scholars. It is valid and proceeds by the ruling of a sharia judge or for those who follow Abu Hanifa.

3. If the woman's brother is the guardian while there are her sons who are eligible for guardianship: This is not valid according to the majority, contrary to the Shafi'is. It is also not valid for the guardian to be a witness at the same time.

If the pillars of marriage are met, then a small dowry or the wife waiving her right to maintenance does not invalidate it.