The key word there is "possible" - dev didn't at any point say the bikini pic was a sneak peek/preview. Someone asked for a pic showing the bikini that gave her those tanlines and dev showed a pic. Given the number of Vivian and non-Vivian pics dev has put out there under "show your skills" etc., and the format of this pic (portrait rather than the usual full landscape render) it might suggest that it's just a random or test image. Obviously though, it could also be a genuine render for the game that's just been cropped.
Not necessarily an in-game render, as above.
I don't think it's unusual for her to say "my son" at all. It's quite natural, as when Hutch is not there, there's no "our" present (saying "our son" in that conversation, grammatically speaking, might indicate she means Christian's and her son!) and it would definitely be odd to say "Hutch's and my son" or whichever way around she might want to word it. She is talking emotionally, and in fear of losing something (someone) who metaphorically "belongs" to her, hence "my".
Again, not necessarily with the bikini, but the twins were talking about going to the beach as well, rather than a pool.
As above. I don't think it raises the slightest bit of doubt, and it's only people trying to pick the minutest detail apart to make new theories, leading to someone coming up with "Hutch isn't Sawyer's father". If it wasn't for that, no one would give this line of dialogue a second glance.