Yes, I also find the flat very curious. OP said she had broken her head trying to understand it and gave up. Also, the paying childcare to ex when he's got the kids 50-50. And paying alimony to ex beyond 5 years, yet she's now trained up and has a good job. It's all so WEIRD.
Add to that his insistence that OP is all about money and that he wants a partner that "shares" everything.
🤔🤔🤔
There could be a benign reason for this - i.e. he has the financial sense of an incontinent gnat. It's not impossible: my father, who was similar to OP's ex in his good looks and charm and looking at women as interchangeable appliances, was really stupid with money. He was a proligate user of people (women) himself, but so vain that he was easily conned. Once he told my sister about this woman he 'romanced' in Indonesia who he gave 5 grand to start a bar. She was a prostitute (which he knew - he was a client UGH) and when he looked her up on his next visit, her henchmen threw him out. (No blame to this woman, good on her). He was hurt! My sister told me this and we were just 😲. And he was - unbelievably - an economist!
So, monumentally financially stupid people do exist. But these are NOT people you want anywhere near your own finances or in a position where the guilt thumbscrews can be put on you to bail them out financially.
Usually, though, when someone tells a story that is simply not logical and you're left none the wiser on questioning - there's something going on that the person doesn't want you to see. Maybe they have a lot of debt. Or some expensive and nefarious past-time (prostitutes, Only Fans, gambling, drugs). Whatever it is, they're hiding it because they know you will disapprove and/or end the relationship. This is lying by omission, and taking away your right to make informed decisions about your life. These people are absolutely not safe to have relationships with.
OP, I don't know which of the two - benign or malign - your ex is, but either option means you dodged a bullet with this bloke.