halaci said:

3. According to the Castle wiki, it was mentioned that she was 29 in the pilot and her mother's murder happened 10 years before (age 19). Somehow I doubt it as her father had serious alcohol problems in the first five years after the murder. I can not imagine that she would leave him alone for a semester while she was in Kiev, so the murder probably happened after this, meaning that she was

I think this is a little shaky. I assume that at 19 you're in university (I'm Canadian and went to school under a different system, so I might be wrong.) Suppose she does a semester in Kiev, comes back, then the murder happens. She's still 19 and what, just finished freshman year? A sophomore? Her father starts drinking, which is bad, but for the first year he assures her things are going to get better and she believes him. It's not until the drinking drags on that she becomes convinced there's a problem. In hindsight, it gets labeled as something that started with the murder but while it was happening, there was a tendency to think, oh, it's just a phase.

I could be wrong, too: there might have been an explicit mention that the murder happened while she was in high school; I don't remember. The reasoning here still works, though: for the first year or two, she is sure the drinking will get better. Her father perhaps hides it from her–bad drinkers have been known to do that–and she goes to Kiev, thinking that everything's all right. It's only when she gets back that it's obvious how far he's slipped.

Just an alternate interpretation.

Just want to contribute that I don't remember ever hearing any reference to age 29 in the pilot either…is there anyone else out there who knows what line that was in? And just out of curiosity, how do we know that she wasn't at the precinct 6 years ago (when was that stated?)  

Personally I always assumed that Beckett was in her early thirties during the pilot. I do agree with the poster who pointed out the possibility of her Kiev trip occurring after the murder, because even if her father had starting drinking it could still have been too early in the game for either of them to realize what a problem it was. Plus, taken in a different light, the Kiev trip may then also have partly been an excuse for her to get away from New York and the painful memories of her mother for a while. However, unless someone can find the explicit reference to 29 in the pilot, that age seems a little young to me. 

If I can get a little obscure and start pulling reference points from else where (because isn't that what we obsessed fans do best?, I'm sure we can go with the assumption that Beckett and Castle must be fairly similar in age. Alexis is at least fifteen or sixteen (do we know her actual age for sure?) That means that if she was born when Castle was around, say, 21, he's at least 36 or 37 now. And if she was born when he was about 24 or 25 (which I personally think is a more likely age, especially given that we have to factor in time for him to have written his first bestseller and dated Kira before marrying Meredith), then he's now 40 or very close to it. 29 and 40 – an eleven year age difference? It's possible, but I think it's less likely. I prefer to think of her as in her early thirties and him as in his later thirties. 

I have to say I'm also intrigued by this timeline and about the idea of how much the writers themselves have considered it. At the same time, I think that with a little tweaking a lot of it does fall logically into place on its own even if they haven't explicitly planned it out in this detail.