Why Keane doesn't have a daughter

As the movie progressed I just became less and less convinced that Keane actually had a daughter, even when he seemed to replace her in his heart with Kira. I think there were more than enough clues to give me this perception:

1. Seemingly the only picture he had of her was an old, small, black-and-white newspaper picture. Remember this is the picture he showed to random passersby in the train station, in order to find anyone who's seen her. If his daughter was real, wouldn't he have much more, better photos of her from before she was lost?

2. When he first approaches the ticket booth and asks if they had seen his daughter, notifying them that she had been taken at that very train station, it seemed as though they had seen him before and were aware of his illusion. Wouldn't they have said something about a police report or security footage or that a search being underway if they actually believed him? It was a train station they worked at after all, so they must've had access to those things somehow. That supports the notion that the picture was someone else's missing daughter torn from a newspaper.

3. He randomly attacks a stranger for "looking at him," when really the man was just minding his own business and making his own separate way. Tackling him and beating him up is more likely to be something to support his illusion rather than to seriously believe the man kidnapped his daughter (though both scenarios could still fit).

4. Even if he did have a daughter, he most likely would lose custody of her due to unemployment and being on disability (he did mention a divorce, so it's possible his ex-wife would have custody). So he could be lying to himself about his daughter being "abducted" all along when really he would know that he lost her in custody.

5. He didn't know his own daughter's dress size so he had to ask a random woman if a dress would fit her daughter since the two are of similar size.

6. Being with Kira would've probably reminded him of his daughter too much, and seeing as the wound is too fresh (he lost her just a few months before) it would tear him up to see her, let alone be with her and be as fatherly as he was to her. Rather, in their scenes together he seemed rather happy and at peace as though he was given a purpose other than being all alone. A random mother and daughter whom he had just met two days prior would not be able to fill the void so soon.