I'm not so sure about the coup. Because it really is not clear. First off, you can not trust one word that Yanukovych says, period. He basically engineered his own election by many accounts; of course whether that is true or not is debatable as well. Second, he was losing badly in negotiations when many of his MP allies were deserting. Third, he left quickly which surprised many in government. Yes things didn't follow all the rules (the rules were written to give president most of the power and to make sure parliament couldn't mess this up).
My theory is that he knew the end was coming. If he lost the elections later in the year (almost certain to happen) he'd have been exposed to a lot of recrimination and prosecution for various misdeeds (all that missing money). So he cut and ran. He wasn't going to stick around for an impeachment.
The constitution is a piece of paper. There is theory versus practice: the theory is the constitution, and the practice is what actually happens on the ground. The parliament reverted to an earlier constitution from last decade. Which is more legitimate than the other? The one he got rid of in order to consolidate more power or the one he replaced it with? Yes at one point there were enough parliamentary votes to bring in the new constitution that is true.
Yanukovych was not the entirety of the government. He has no authority to ask Russians to invade on his behalf. Even if he was still in office he did not have that power as a single person, even with the greatly expanded presidential powers that were added to the constitution while he was there. What he says now is irrelevant. You either assume the current government is legitimate or illegitimate, Yanukovych is out of the picture.
So maybe it was a coup. So what? It gives no extra power to Putin, except an excuse to use his military (I say "his" purposely, most people in his government appear to be his assistants rather than his limits to power). A coup gives no extra legitimacy to Yanukovych either.
Some part of the Crimea wants the Russians out of there too. There is no basis in any treaties for Russia to put troops outside their bases and surrounding zones in Crimea, the treaties are clear where the boundaries are. Going all the way up to the gates of Ukrainian military bases are most certainly not allowed in the treaties. It's clear that this will end badly. Tatar houses are being marked with the same symbol that Stalin used before deporting them, as an attempt by some people there to intimidate the minorities. No way are these pro-Russian fascists going to be singing kumbaya with their former neighbors (yes, people on both sides can be fascist), there are signs this could play out like the breakup of Yugoslavia.