When Obama wanted to get chemical weapons out of Syria, Putin took the leadership role in doing so. As a way of criticizing Obama, McFarland said that Putin "was the one" who should have gotten the Peace prize - e.g., between the two of them, Putin was getting more done for peace in this situation. She wasn't saying, in a vacuum, that for all his government's actions Putin should be rewarded with a peace prize.
No. Despite what Trump's advisor says, Vladimir Putin does not deserve a Nobel Peace Prize. He is responsible for atrocities including Russian airstrikes on Syrian hospitals and other civilian targets. He also seized Ukraine's Crimean Peninsula in a despicable showing of modern-day colonialism. This is not behavior that is becoming of a Nobel Prize winner.
Putin has been responsible for causing enormous civil unrest in Ukraine after the annexation of Crimea. While the right to self-determination for the Crimean people is important, Putin essentially used their Russian ethnicity to punish the Ukrainian government for leaning towards EU membership. This was an impetus and reckless decision that has cost a huge number of lives.
Putin does not deserve a Nobel Prize. Among other glaring disqualifications is the Russian invasion of Crimea and the Russian involvement in the Syrian civil war. Crimea was a sovereign nation and should have been left to decide its own fate domestically without the Russian intervention. As for Syria, the fact that food convoys and relief hospitals have been bombed by Russians or with their acquiescence is enough to disqualify Putin for the Nobel prize.