I will answer these out of order sorry.
2- There is no real answer to this but I will tell you how I interpreted it. I believe that both the Alpha and Steins gate world lines are actually conneted before Okabe's fist encounter with Kurisu. Once he interacts with her in the anime it creates the Alpha world line and then when he sets the steins gate I believe that it is bassaly a fork in the road. Let me explain a little. In the anime when Okabe kisses Kurisu he talks about how it will not be stored in his hippocampus because it is not his first kiss. I interpret this as he remembers his first kiss with Kurisu but does not know that it was actually her. So in both the Alpha line and Steins gate he remembered the kiss but in steins gate he remembered that it was her so that is what tied him to the Steins gate line.
3- I dabbled on this in number 2 but I will explain a little farther. In both lines he remembers having a first kiss before going to get Mayuri, but the difference being that in the Steins gate line he remembers the significance of that encounter. In the Alpha line he most likely just remembers a kiss but nothing else. The difference is that in the Steins gate line he remembers who gave it to him and the story that Kurisu gave him about his future self. This is most likely what grounded him to the steins gate line.
Last but not lease 1- This is kind of a blurry spot. I'm not actually sure if in that time if she looked like her 13 year old self of if that was just something they added but I have 2 theory, one more unlikely then the other. Most likely this is just something done by the producer but I hate that so I came up with another theory. This is very unlikely, its actually probably impossible but it could be that when Kurisu went back in time to when she also would have been 13 that everyone saw her as the age she would have been at the time. For example, if she were to go to a time where she was just 5 then everyone would see her as a 5 year old. This is most likely false due to the fact that Suzu was from the future but looked her actual age. Think what you want but when producers do things like that it bugs me so I to would like an explanation.