At the risk of sounding like "I love your idea but here is how to change it to something I like better that is completely different and nothing like your original idea", here are my (unsolicited) thoughts: The prompts didn't really resonate with me. I don't really care about who someone who haunt as a ghost or what kind of animal you wish you were. I want to check in with friends not share BuzzFeed survey results with each other. That makes more sense in a dating app or ice breaker imo. As far as the pictures go, I would actually prefer that it was only one and mandatory. There feels like there is something compelling to find the picture that best represents your week. Whether that is a picture of your dog or a landscape or a meal you cooked, etc. It also forces you to create an artifact that captures your week. There are lots of weeks where I normally take zero pictures and this could be a nice nudge to force me to pick a moment but not feel like I have to document everything.
I design board games a hobby and am part of a group that has a short weekly accountability meeting once a week. It is structured like a stand-up in some way. Each player says what they worked on last week, what they hope to work on this week and what they could use help with. This is the kind of status that I'd be interesting in both sharing with friends and reading about theirs. The "needs help" part is a perfect specific reason to reach out directly. I also like that this feels a little bit like journaling and even if you don't get friends to join the network, you still have a weekly recap of your year. (Honestly, I could even see a paid product that creates a 52 page book/pdf for you to review and see how your year went and where it went wrong.)
Definitely good potential here, so best of luck on the journey.