Not happening.
Ukraine may be able to get EU membership, but I expect any deal will include wording that keeps Ukraine out of NATO permanently.
Trying to push NATO closer to Moscow is part of what spurred on Russian actions in Ukraine for the past 8 years.
Possible; we'll see what happens in the next few days.
No, the hostilities, on political-economic arena at least, have started with the EU association treaty related embargo, still under Yanukovych.
The whole NATO question is a semi-understandable excuse used by Moscow to cover hard XIX century style imperialism, mostly meant for gullible westerners. There isn't that much focus on this excuse domestically.
That's why their "ideal" plan was a shock&awe campaign to both take over vital pieces of land for further incorporation into Russia (DNR/LNR region, Crimea land bridge), while installing a puppet government who will rubber stamp these border rearrangements, at the same time somewhat solving the issue of Crimea sanctions in light of the land grab not being recognized, and lets not forget the demilitarization demand, aka ensuring that in case Ukrainians get ideas again any not sufficiently obedient government can be yet again special operation'd away with preferably very little effort in the future.
As such, even as a minimum option, Russia is going to be really unwilling to even formally accept Ukraine's EU membership, and even then, it will strive to leave a "try again later" button available by trying to get in the way of any external security arrangements for Ukraine, to use it before Ukraine actually joins the EU and "renegotiate" the deal in more favorable circumstances.
So far i don't think Putin is seriously considering any scenario where he backs down and cuts his losses, and won't do so as long as the military situation leaves any sliver of hope that they can keep an advance going enough to get one of the ultimatums accepted.
Getting the words 'denazification' and 'demilitarization' removed from ceasefire talks, while also not trying to keep Ukraine from joining the EU, is at least a step in the right direction.
Those terms appear and disappear now and then, proving what some say, these negotiations aren't achieving anything now because Russian side is meant to not achieve anything. They are just running out the clock in hope that at some point they get into a position where they can get away with negotiating through demands and ultimatums, that's when they will we seriously willing to take a deal, which is going to be their own ultimatum.