7. Why does Russia care so much about Ukraine?
There are the surface reasons. The cultural connections are indeed deep, and Putin can't not want to remain close to a country with so much shared history and so many Russians. The country, a source of food and a transit hub for Russian energy exports, is economically and strategically important to Russia. Putin is thought to personally care a great deal about the Eurasian Trade Union and sees it as his legacy.
And then there are the deeper reasons. Ukraine makes or breaks Russia's self-image as a great power, which has fared poorly since the fall of the Berlin Wall. As Tufts political scientist Dan Drezner put it in Foreign Policy, "For all of Putin's Middle East diplomacy, Ukraine is far more important to his great power ambitions. One of the very first sentences you're taught to say in Foreign Policy Community College is, 'Russia without Ukraine is a country; Russia with Ukraine is an empire.'"
Even if Putin can't bring Ukraine in, he'd like to keep it out of the European Union, which he sees as an extension of a century-old Western conspiracy against Russia. There is a certain lingering suspicion in Moscow that the West wouldn't mind Russia's destruction, which is part of why it so opposes any Western intervention into another country, which it fears could be precedent for a similar attack on Russia some day. This is why, silly though it may sound, some security experts tend to emphasize Ukraine's importance to Russia as a defensive buffer.
8. Why haven't the U.S. or Europe fixed this?
Western countries could pressure Yanukovych to halt his authoritarian-tinged actions since the crisis began (the Ukrainian parliament rolled back most of the anti-protest law on Tuesday). But most of the power seems to be with Putin and with actual Ukrainians, so it's not clear what the West could do. A New York Times op-ed by four (four!) former U.S. ambassadors to Ukraine mostly just called for the U.S. to issue statements, adding that it could follow those up with economic sanctions.
The danger though is that any Western action strong enough to make a difference could risk a backlash that would make things worse. If the West gets too aggressive about pushing Yanukovych, then the country's eastern, Russian-facing half might see it as foreign meddling not so different from Russia's involvement.
Ultimately, the deeper issues here are Ukraine's troubled economy and its unresolved national identity. Outside countries (including Russia) can certainly help with the former, but the latter can be solved by only Ukrainians.