Solved

Has earned without use of a proxy, vpn and Opera Turbo. The websites open.
Все заработало. Без обновления браузера. Значит была проблема на стороне opera.

Now and through a proxy doesn't work.
Chrome and Chromium works.
Проблему решить не могут почти две недели. Пора менять браузер ( ?

avl, vpn and Opera Turbo turned off. Russian Federation.

Using proxy solves a problem
(https://antizapret.prostovpn.org/proxy.pac)

40.0.2308.81

up

OS: openSUSE 20161003 /Fedora 24 etc
Kernel: x86_64 Linux 4.7.5-1-default
Shell: bash 4.3.46
Resolution: 1280x1024
DE: KDE 5.26.0 / Plasma 5.7.4
WM: KWin
CPU: Intel Celeron CPU G1610 @ 2x 2.6GHz
GPU: GeForce GT 440
RAM: 2831MiB / 13989MiB

Opera 40.0.2308.81

Not open www.dropbox.com, https://auth.opera.com/account/login?service=forums&return_url=http://forums.opera.com/category/43/русский and etc.

Using a proxy server helps

Error:
This site can’t be reached

dropbox.com took too long to respond.

Try:
Checking the connection
Checking the proxy and the firewall
Check your internet connection.
Check any cables and reboot any routers, modems, or other network devices you may be using.

Allow Opera to access the network in your firewall or antivirus settings.
If it is already listed as a program allowed to access the network, try removing it from the list and adding it again.

If you use a proxy server...
Check your proxy settings or contact your network administrator to make sure the proxy server is working. If you don't believe you should be using a proxy server: Go to the Main menu > Settings > Change proxy settings... > LAN Settings and deselect "Use a proxy server for your LAN".