1. You are perceptive, this is usually something to watch out for. However, it does not always indicate that a study is flawed, just that the research might have met with unwanted resistance, and the authors are in position to avoid that resistance.
2. Yes, these scientists are looking to make their research popular, highlighting an unfortunate conflict of interest present in academia. They do this to get big grants. Important observation, but insufficient to dismiss a finding out of hand.
3. So many authors, such a joke! These people mostly just help collect data, or sometimes simply share data they already have and then give the manuscript a quick read before publishing. But that is actually beside the point. If a lab already had data ready, and isn't pressured to add authors for political reasons, then two authors is not necessarily a red-flag. In fact, these analyses are relatively easy to do with available software. If they have the data, they just plug and chug.
4. The findings of the paper suggest strongly that friends are more genetically similar, on average, akin to fourth cousins. The results have yet to be rebutted to my knowledge. The fact they found some regions were negatively correlated does not conflict with their overall results. I have some doubts that their regional analyses should carry much weight (e.g. olfactory and immune regions). Furthermore, their explanations using natural selection appear to be a stretch. These are possible overstatements of results, allowed because of your points 1 and 2.
My overall impression of the paper is that main results are somewhat interesting and entirely novel. But there is a ton of stretching for just-so stories and "interesting" findings that will be unlikely to hold up. Typical PNAS.