Last one sucks.

As for the rest, Putin at this point must know most of this. You need a sh*tload of superiority and motivated soldiers to assault a defensive position, not to mention supplies, communications and the ability to use combined arms effectively.

At this point, Putin has understood he cannot operate further than 150 km from Russian bases. He must also be well aware of the real performance of the Tactical Cannon Fodder Battalions and even the Airforce and he must know the number of casualties (some mention 20% of troops and means). He must hold little faith on the ability of his army to "blitzkrieg".

So, what is the strategy now? My two cents:
- Consolidate, make modest gains if possible and let the other side be the one that has to assault fortified positions.
- Sell the territorial gains in the south and east as the Victory.
- Negotiate minor concessions in exchange for the lift of sanctions (maybe).
- Make the scale of the war and the costs more manageable and sustainable with a depressed economy.

An for Ukraine:
- Stop any salient attack in the East and prevent encirclement.
- Push back where possible  (this would require a significant western support, that seems to be happening at some degree).
- Unfortunately, cause as many casualties as possible to the invader.
- Keep promoting isolation and economic damages for Russia. Ensure time plays on their side.