danken- to thank
gehören - to belong
helfen - to help
Here is a link with all of them
I think your learning takeaway could be to try and work out the possible declensions, as ihren couldn't make sense here with the verb helfen as possessing a man (in Deutsch) typically makes him married to you, and you wouldn't really have multiple husbands... (ihren only being able to be the "her/sie" in plural dative). And the only other time we use 'ihren' is "her/sie" in akkusativ singular masc and helfen must be used in the dative case.
Or could be a Non binary person who uses the pronoun "They" married to a guy.....
Not on this course -- we don't use "singular they" here.
English speakers have enough trouble differentiating "singular you" from "plural you" in German (du, ihr), and distinguishing between sie ...t (she) and sie ... en (they) that allowing "singular they" would cause more confusion than help.
Can "ihr Mann" only refer to a married couple? What about a boyfriend?
"her man" implies they are in a relationship, although not necessarily that they are married.
Also, what would you say if it was like an employee or something of hers? For example, an underling might be referred to as "my man", "his man," "her man," depending on who the boss is.
Can "ihr Mann" only refer to a married couple?
(Well, almost all of the time. Some people might use mein Mann even if they're not married, a bit like I've heard "my hubby" used for someone to whom they were not married. But in general, mein Mann implies marriage.)
What about a boyfriend?
That would be ihr Freund.
Or for a more long-term but unmarried relationship, it could also be ihr Partner or ihr Lebensgefährte ("her life companion") or various other terms.
I thought that the dative case for "she" was "ihr"
That is correct -- like how in English the dative case for "he" is "him".
But "him husband" or "him wife" would not be appropriate here -- what we have here is not the personal pronoun he/him or she/her.
The "her" in "her husband" is not a personal pronoun; it's a possessive adjective or possessive determiner.
It's a bit confusing that in English, "her" is both a personal pronoun and a possessive adjective -- thinking about whether to use "him" or "his" instead may help to distinguish them.
The possessive adjective "her" in German is ihr -- but before a noun, it needs an ending that depends on the gender, number, and case.
Mann is masculine, so in the dative case (while helfen requires), ihr turns into ihrem with the masculine dative ending -em.
what determines the gender of the possessive dative? Is it the gender of the noun it is attached to, which seems to be the case here, or is it the gender of the to which it is being referred to by this possessive adjective?
The stem indicates the gender of the possessor: sein- "his" versus ihr- "her".
The ending indicates the gender of the possession: -em for masculine or neuter dative, -er for feminine dative, -en for plural dative.
seinem Messer und seiner Gabel "to his knife and his fork"
ihrem Messer und ihrer Gabel "to her knife and her fork"