Nowhere in any of your posts do you mention being in love with this man, having any consideration for his thoughts and feelings, etc...
Anyway, most mortgage lenders who do buy to let will require you to have your own, or joint property that you live in first. Its not exactly hard to find this out by googling buy to let mortgages or the main buy to let mortgage lenders. Since you have a phd, I'm surprised if you were genuinely interested, you haven't done so already.
Perhaps in real life you are a lovely genuine person but on here you have come across as money oriented and have been abusive to posters who don't agree with you. You must surely realise that most women who have been to university generally go for the sort of relationship where they are equals with their partner and see nothing wrong with paying their own way in life, even if they choose not to work after having DCs, at least for a little while. I would think mumsnet has a far higher than average number of SAHMs, as many women in work won't have time to post. Even so, people have been pointing out to you its better to be self supporting if you possibly can. You have the benefit of a lengthy education - what was the point in getting that phd? What example are you setting to your DC if you under-achieve and expect others to prop you up financially?
Your post just drives home what a hassle and a strain organising your life in this way must be. Working and getting your own mortgage is so much easier - I am the same age as you and it was easier to buy property then. I think if I hadn't done that, I'd be doing everything I could now to stay in a secure job and buy my own place. This man would be a fool to sign over the rights in his property to you, and he sounds about as willing as a lamb being led to slaughter. Would it not be easier to start again and try to find a man that loves you and wants to marry you, instead of trying to force an unwilling one into it? Its undignified. Your various posts on here make you sound so unhappy and terribly insecure and frightened of the future.
As for your costs. If you have paid half the bills, you would have had to pay your own bills anyway if living in your own place. Extra food for one person isn't that much, certainly not as much as paying rent or a mortgage for your own place. Even 5 years at £400 a month rent would be worth a saving of around £20,000 on your part, so even if you live in Scotland, I can hardly think that you have been economically disadvantaged and can make some claim beyond child maintenance. I don't feel that sorry for you though, since unlike many other women, you do have a good job and education.
If this man is really considering signing the agreement you have drawn up, he really needs to get independent legal advice, otherwise it risks being challengable on grounds similar to undue influence or coercion, depending on the exact situation.