He destroyed an entire region of his own country (Chechnya) in order to save face. He views Ukraine as a rebellious region like Chechnya which must be put down by any means necessary.

The evidence is there, if you care to look. Frankly your distrust of social media is tending towards paranoia - civilians don't have the means or inclination to mass fake videos, I'd say most are valid reports. Yes videos will be mislabelled (e.g. wrong region) and repeated without question sometimes, but some of the evidence is very clear and very hard to fake.

I believe the fastest way out for Ukraine is to give Russia a guarantee that it will not pursue NATO membership (I understand this is all that Russia wants and has been asking since the 2014 coup that removed the Pro-Russia government), ensure Russian-speaking citizens in Eastern Ukraine will not be prosecuted, and acknowledge Russian rule over Krimea.

This should absolutely be acceptable to Russia, and while not being great for Ukraine, it's still better than a prolongued war with Russia and the chaos that will follow even after the war finally ends (with Ukraine's infrastructure most likely almost entirely destroyed)...

Why I think this should be acceptable to Ukraine? Because Ukraine has always had a "blurry" border (this is the same all over Europe, by the way! The very notion of statehood is a 19th century concept in most of Europe) with Russia. Losing a small part of its territory shouldn't be such a huge deal - it's less of a deal than having its cities bombed to the ground and its population fleeing for their lives for years to come, at least.

Accepting to not join NATO is a greater problem as that practically means the threat of aggresion by Russia will continue. But the alternative, Russia NOT having a say and "allowing" Ukraine to join NATO has already proven to be unacceptable to Russia to the extent it's willing to destroy its own economy to prevent that from happening (it might even use nukes, as Putin made clear already). However, this is something that with a few decades of careful negotiations with both sides can actually end up benefiting Ukraine! How? Ukraine will have leverage on both sides: the West does not want to let Moscow have a say in Ukrainian affairs, specially after this aggressive war, while Russia will have no choice but thread carefully with its businesses in Ukraine, trying to keep Ukrainians happy enough to not want to overwhelmingly join NATO and "fight" with Russia. It's unfortunate that the governments in Kyiv since 2014 have not been able to play exactly this game and have instead let the situation deteriorate into a war.