For the fakes dilemma, there is a section on this board called "Tamagotchi Warnings" that you can visit. It'll alert you to some of the fakes people have seen around. The bottom line though is that if it says BANDAI on the package you purchased AND on the back of the Tamagotchi egg (you will probably also see the year in which it was made), the Tamagotchi that you have is not a fake. That's the key...always look for the BANDAI logo printed on the package and the Tamagotchi unit.
As for the V2 and V4.5...I was under the impression that they aren't compatible to mate. If I am wrong about this, someone can correct me (I barely play with my V4...I prefer the Tamagotchi that came out in the 90s). Anyway, if they are compatible to connect, just wait until both have spent at least 24 hours in their respective adult stages and make sure they both have established a good relatioship with each other (the friendship heart level). That's all I can think of for the conditions of mating.
What do you mean your V2 mated twice? Do you mean one after the other, right away or it mated once and then a few days later, it mated again? If it's the latter case, then that's normal because as long as you take good care of your Tama, it's going to keep mating and continuing on the generations. I mean, that's the whole point of Connections...is to keep on connecting and mating and getting as many generations of Tamas as you can.
Growth charts: I don't know which one you're looking for because you didn't specify but you can always try the LIBRARY section on these boards and go to the Reference Section. Here's the link (isn't it great that you can find everything you need on Tamagotchi just by browsing this site? Amazing!):
https://www.tamatalk.com/IB/index.php?showforum=29
Here's a link to a V4.5 chart:
https://tama-zone.com/index.php?showtopic=15082
Hope this helps and good luck!