Just keep trying. If you unpack the images, you can get a hint at the general location of where the magazines are depending on the image of the secret in the location folder. I can tell you the one in the front garden is near the plants iirc and the one in the MC room is under one of the location icons.
Nina update (which will include this quest I assume) is planned for 15/09, this was the Mia update.
Time limit is mostly there because certain events are time-based (ie you call Mia on Wednesday, she calls you Friday/Saturday). In a way it doesn't really matter because saves aren't compatible, but if you just endlessly stretch out time it would probably create a mess as well. I also think that most of the things are pretty easily accomplished in the given timeframe if you know what you're doing.
Yes.
Think this will get added with the public release or 0.4.