2. I read it differently. The screws are tightened and company will be under control of board if Volozh dies, 2 of 12 board members are government-appointed. So I agree that government is trying to control Yandex tightly. It hasn't happened yet.
3. As far as I can see - Yandex does not support the war. And no russian commercial company can be openly against the war without effectively stopping the opperations immediately. Living under insane dictator is hard, but I don't think it is reponsible behaviour to turn shareholders investments into nil, leaving 20k people without job and millions of people without services (the last part is the least important because there are other local substitutes for most Yandex services). Genuine western companies can be openly against the war, because neither sufficient part of their income comes from Russia, nor most of their production/workforce is in Russia.
About your small things:
1. What kind of news can be aggregated from other sources is regulated by law. I mentioned that in my firs comment. There are _no_ non-pro-government news sources left in Russia. The ones that were still operating a short while ago regularly recieved strikes from regulators. You could make a point that it would have been better if Yandex just closed its news service entirely; and I would agree with you. I bet Yandex is thinking the same right now, but it is hard to make this decision when things were slowly regressing for 10 years and the tipping point was reached and news became toxic.
2. Right, because making statements to Putin makes such a great difference?
P.S. It is quite clear that in the recent years Yandex was trying to migrate from Russia as soon as possible to be less dependent on the whims of the regime. They did find the niches where they could be successful outside of Russia (at the very least - delivery, taxi and ride-heiling, cloud) but didn't have time to execute the plan.