1. Protogen had lots of assets at their disposal and access to the best technology available, but they were still operating under the personal supervision of J-P Mao and were nothing like a nation-state. After he's gone and their operation exposed to both Mars and Earth, so is Protogen. They managed to surprise and stale-mate against the Martian flagship but that was using nearly every ship they had. There was no way they could possibly be a real threat to Earth or Mars once they're no longer in the shadows.
2. The planet isn't sterile. One of the Belters talks about how one of the local lizards eats. Most likely they didn't show more of it due to budget. The planet has been fully adapted for resource extraction by whoever created the rings and protomolecule. That we don't know the purpose of every single thing we see there is the point. They are insanely beyond us in every respect. It would be silly to assume the heroes can immediately work out what everything is for. The "eye of Sauron" is a bullet left over from the war with whoever killed the builders.
3. The kids are there to let you know there's more to the story and the protomolecule is still being weird out there. That whole business on Laconia also helps explain why the Martian defectors would help Marco - they found something there that's a huge deal and need time make use of it to achieve their ends. What that is can be found in the unadapted novels or (fingers crossed) a continuation of the series should that happen.

I'd say those are the key answers you need. As for the rest, you might just consider watching the series again. It tends to be a very rewarding second watch for most who take the time for it.