See the above link for (1).
The "uphill struggle" referred to in the link, about a share in the property, means an action in equity, that part of the law that exists to rectify wrongs created by a literal interpretation of documents and statutes. She would need to show that it was manifestly unjust for her not to be given a share in the house. To do that, she would need to show that she had made substantial contribution , not necessarily expressed in terms that it was to pay for the house or the mortgage. It could be that without it, he would not have been able to pay for the house or mortgage, however it was expressed, if expressed at all. Alternatively (and highly unlikely in this case; it's meant for other cases) the claimant would have to show that she was promised such a share and, in reliance on that promise, had lived in the house, to her own detriment when the promissor reneged on the agreement.
All this fuss, and all the expense and doubt as to the outcome, would be avoided if women were not so naive as to believe the old lie "a marriage certificate is only a bit of paper" usually followed by " we don't need one to prove our love"