For South Ossetia, Abkhazia and Pridnestrovie Russia has NOT annexed them, even if they probably wouldn't have minded (not sure what the situation is...)
So what would be different about this, if anything?
Sure enough, Crimea will become a part the Russian Federation.

The propaganda war against Russia is overwhelming at the moment. Will this affect Russia's response?
Certainly, the wording “in response” will be rather strong but not that aggressive as you can imagine.

Could Russia just reject their request to join the federation?
Are you kidding?

How much would it upset the new Ukrainian government, regular people in Ukraine and the West?
They will have to put up with the fait accompli in the long run. Khrushchev giveth, Putin taketh away.

Could this lead to war?
Only in case the USA should make such a snap decision as to send its troops to Ucraine