Q: Browsers opens only https sites over wifi.

Hi,  you can try some troubleshooting steps:

Reset SMC

• Turn off the MacBook Air or MacBook Pro
• Connect the power adapter to the Mac as usual
• On the keyboard, press and hold down the Shift+Control+Option keys and the Power button at the same time, hold them all for a few seconds
• Release all keys and the power button at the same time by lifting your hands away from the keyboard
• Boot the Mac as usual

You can also try to reset your browsers and restart your Mac.

Safari:

Go to Safari menu (At the very top right side of your screen next to Apple icon), choose "Quit Safari"

press "Shift" button and while holding this button on your keyboard single click on the Safari icon on your Dock.

Open Safari - Preferences - Privacy - Remove All Website Data.

Open the Go menu with Option (Alt) key pressed - Library - locate Safari folder and move it to your desktop.

Google Chrome:

https://support.google.com/chrome/answer/3296214?hl=en

Firefox:

https://support.mozilla.org/en-US/kb/refresh-firefox-reset-add-ons-and-settings

Try running this program and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown.
  

Etrecheck – System Information

Safari - Unsupported third-party add-ons may cause Safari to unexpectedly quit or have performance issues

Safari doesn't load a page or webpage items are missing

Safari/other browsers – Website not loading