Finland and Sweden have realised that NATO and the EU are one and the same. They had already been forced to participate in NATO's economic war against Russia (aka "sanctions") so they might as well take the official step and at leat get some of that sweet US aid money for weapons and such.

And yes, Crimea is as much a part of Russia as Moscow. Catherine the Great won it from the Ottomans in 1774 and it has always been an important destination for Russian royalty, elites, writers and artists, etc.

As far as Putin's intentions are concerned, you can see them here:

https://web.archive.org/web/20220203093936/http://en.kremlin.ru/events/president/news/67402