Safari 9 doesn't open some even major sites. Chrome, FF -- ok.

With Safari 9 (extensions off), after upgrading it and OS to El Capitan emerged these problems:

1. When trying to open some sites that work fine with FF and Chrome Safari shows:

"Safari can't open the page. ... can't establish a secure connection".

Messages from the console:

15/10/15 10:02:40,483 WindowServer[154]: _CGXRemoveWindowFromWindowMovementGroup: window 0xed6 is not attached to window 0xf1e
15/10/15 10:02:40,764 com.apple.WebKit.Networking[1805]: CFNetwork SSLHandshake failed (-9824)
15/10/15 10:02:40,765 com.apple.WebKit.Networking[1805]: NSURLSession/NSURLConnection HTTP load failed (kCFStreamErrorDomainSSL, -9824)

2. Sometimes when trying to open some sites like Twitter, and even Google, when making query to Google from the address line Safari freezes, shows blank page, blue bar doesn't move. In these cases the console shows something like that:

15/10/15 10:12:02,117 WindowServer[154]: _CGXRemoveWindowFromWindowMovementGroup: window 0xed6 is not attached to window 0xf1e
15/10/15 10:12:04,330 com.apple.xpc.launchd[1]: (com.apple.WebKit.WebContent.5F9745D8-A375-4A2D-9614-275BF8C5334D[8978]) Service exited with abnormal code: 1
15/10/15 10:12:07,677 WindowServer[154]: _CGXRemoveWindowFromWindowMovementGroup: window 0xed6 is not attached to window 0xf1e

I've searched the Net and this forum and couldn't find any firm solution to this problem despite the fact that there are a lot of similar topics started.

There's something wrong with Safari 9 and I can't believe there's still no solution.