Well I'm not the topic starter, but live in Russia as well and can try to answer from my perspective.

1. I don't. Lot's of people are in favor of Putin and politics Russian government carries. It happens because of various reasons. Massive propaganda is one of them. Anything against the current political course is forbidden. Most of tv time is given to propaganda shows and news. I can't really say that there is majority in favor or against because everyone against has to stay silent and everyone in favor can scream as loud as they want. People with anti-war points can be prosecuted even for statements in private conversations or chats. And besides, revolutions are not organized or carried by masses. They are made with money and massive help from outside. I don't believe that any of these processes is happening right now in Russia.

2. Yep, that's exactly what they do. News mostly contain of war success stories (if any), some dad jokes about Biden or other western politicians, some worst stories from US or any European country. Like some ridiculous woke story or shoplifting in LA or even fires. And there always will be some connection to military help to Ukraine. Not exactly fighting for the motherland, because there is no actual existential threat so far. Some Kursk land was occupied but it is not widely covered because it is an obvious military fail. Narrative is more like fighting for peace in Donbass and Lugansk against Ukrainian nazis and NATO mercenaries and NATO weapons which wants to surround and weaken Russia. So as it is a mixture of nonsense and some reasonable things (which do not justify the invasion obviously), but still makes it easier to flush the brains.