Try bringing up the Safari-menu Preferences option, click on the Advanced tab and click the Proxies Change Settings button. All of the check boxes should be unchecked normally and in the box below it should only read as follows normally:
*.local, 169.254/16
Is this already the case for you?
If you click OK or Cancel this pops you into the Network screen. Is your Wi-Fi showing as connected and and the very top of the list? If it's not at the top of the list click on the gear icon below to Set service order and drag your Wi-Fi to be the first item in the list.
Also, in Safari-menu Preferences click on the Extensions tab and try un-checking any extensions you have there.
If none of this helps restart your MacBook Air in Safe Boot Mode (holding down the SHIFT key when you first turn on for 30 seconds) and see if your Safari works properly in Safe Boot Mode. If so, restart and see if it's working properly in normal boot up mode.