Some guys asked me to provide some proofs. Here they are. And as problems happen at almost the same time, I guess it's regular problems.
Video
My logic behind conclusion, that it's server lags:
Problems with my computer would either be
1) Load-based
2) Persistent
Neither pattern is observed.
Problems are more
1) Time-based
2) Location-based
Sometimes there are no lags, sometimes there are. There are no lags in some locations, but there are in some other ones. Yeah, overcrowding causes more lags, but yesterday there was just one player near me. It's not enough to cause such major lags, as server only sends data about objects around me - not location-wide data.
So problem lied somewhere outside my computer.
And only place for this problems is - my ISP. But any ISP latency or packet loss would cause higher ping. And it's also not observed.
Another evidence - such problems would also affect other online games, but they don't.
So only place remaining - is servers themselves.