just a point: putin won power mainly because he promised to deal with the chechen problem. thats why they are blaming him. if you promise something you had better deliver.
and islam is a major factor in these events, especially in justifying the actions to the perpetrators ('we are doing gods will!', kind of thing) but it isnt the only cause. you cant pretend that the chechan situation isnt a big factor in this attack.
i see articles which want to go 'its all islams fault', but they are as wrong as the articles that say it isnt islams fault. islam is the connection between most of the worlds terrorism (i saw some list the other day of the last few years world terrorism and maybe 3/4 was islamic) and isnt so much the cause, as the catalyst.
This instance of Islamic terror in Russia has been called "Russia's 9-11" by many different news services. You are quite right that there are several things at play with Chechen terror. The reason that this is very different from 9-11 is that Chechens are part of Russia.
This would be like, in the U. S., the state of Florida wanting to cecede from the Union and sending terrorists to blow up schools and children in Georgia. We know that this would not ever happen because we are a civilized people. However, Muslims are, for the most part, barbarians living 1000+ years behind the rest of mankind. So they will deploy all sorts of barbaric tactics to achieve the end they desire. Is is not Islam's fault that the Chechens are seeking independance but it is Islam's fault for the methods they use.