What is the significance of a Moon conjunct North Node in relationship synastry?

Its very good to have this aspect. Its one of the major signs of what they call a karmic, past-lives relationship. The north node is where you are headed in life, and where your future lies, whereas the moon is the core essence and being of a person, their nurturing side, and a huge aspect of someone's personality. If it goes both ways in the synastry, it means that you are both meant to be in each other's lives for a very significant reason. You both will feel like the relationship was "fated" and you were truly meant to be together.

Its already considered a powerful relationship if it's the north node making some aspect to a personal planet i.e. mercury, venus, mars...but if its the moon its doubly important and the conjunction is the most powerfully felt aspect, so I would say this is a great indicator of a soul mate relationship, if there is such a thing.

Moon is synonymous to south node. Check her descendant too.

I'd the moon is the one receptive here, Node north is the instigator here. Wherever he is, it is his life goal. So he's the one initiating and the moon responding to his energies. Emotionally compatible? yes bery. Connection? Um yes but not so much as other placements i have in mind if you mean destiny and fate, like vertex aspects in the synastry

If by "both ways" you mean her north node conjuncts your moon too then this is a very healthy relationship, unlike moon/south node's feeling of being "sucked back in". Buoyancy is strongly indicated. I think you both need some connection indicated elsewhere in the chart, to balance out just feeling majorly like Up Up and Away. Some sort of fall-back so to speak.

It's not important. Aspects between planets are important in synastry. The North Node is not a planet.

Holy jumpin' gibberish, Batman!

I don't know, but you should probably consult a doctyor