Jaysh al-Fatah - a radical Islamist organization fighting against Assad in Syria - claimed responsibility for killing the ambassador. The Turkish police found Islamist literature in the murderer's house. 13 people are arrested, mostly his family.
The Turkish officials said the street where the Russian embassy in Ankara is located will be named after Andrey Karlov.
They also blame Gulen, but Gulen condemned the crime too and expressed condolences do Karlov's family.
I don't think so. The Turkish government is cooperating with RF here, promised to punish everyone responsible and the police is looking for the culprits (at least it looks so).
The Turkish embassy in Moscow is taken under reinforced security, too.
Generalization reminder.
By using "the Russians" here, you might be misleading the readers.
Yes, there are some people who suspect the Western powers of this. A Kremlin senator said he assumes so, the journalists are speculating about this (they wouldn't be journalists if they didn't), and Zhirinovsky told that too (which is not surprising at all, this man is a kind of clown). But on the high diplomacy level, no one accused NATO or US or any specific country, neither the president, nor the Foreign Ministry. They only said it was a 'provocation to destabilise the Russia-Turkey relations'.
However, since Jaysh al-Fatah is backed by Saudi Arabia and Qatar, that are allies of the West, that statement may have some sense.