I assume your third link was meant to be to this study: https://web.stanford.edu/~gentzkow/research/facebook.pdf

My first criticism would be that intervening only to restrict Facebook would likely just result in a substitution effect, with instagram, snapchat, youtube, reddit, etc filling the void. Likewise, if I remove cake from my diet for 4 weeks but make no restrictions on all other forms of sugary baked goods, I'm not likely to see the same magnitude of effect as I would've otherwise.

Here's an associational study that found almost 3x odds of having depression between the most and least frequent users of social media sites. This was among US adults aged 19-32 and adjusted for age, sex, race, relationship status, living situation, household income, and education level https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4853817/