Yay, thank you everything works fine now! 

I just disabled Autoptimize plugin. 

Say, is there a way to disable moderation? I want any user to be able to leave comments on my forum without moderation even if he is not logged in. 

Dear  petegrig,

Please read this support topic:

https://gvectors.com/forum/general-questions/turn-off-moderation/#post-4556

Thank you for the link. 

Haha, I have that problem with squares instead of icons again. It worked for about half hour and then again – squares instead of icons. Although Autoptimize is still disactivated. Do you have any other recommendations?

It means you have cache problem. Please disable all caches and autopimization functions for forum page. wpForo has built in cache system. Also if you have CDN, make sure it's fully purged.