yellow card for faking injuries…and for protesting with the referee.

Huge yes. I support the others saying it could even be a red card. The astonishingly bad sportsmanship from soccer players compared to other sports is a big reason it will never be taken seriously in countries like Australia. Diving is nothing short of cheating, and it's developed to such an extent that even children are frequently imitating the stars they see on TV and doing it in local club games.

In Australian football, which is played on cricket ovals ranging in size, but ~150 m long is a good ballpark figure, it takes very little talkback to the umpires (tbh, I've seen the rule overused in cases where it really didn't seem appropriate) before they'll march you 50 m. The opposing team gets not just a free kick, but a free kick from 50 metres closer to their offensive goal than where the original infringement took place.

Football: proper helmets

Assuming you mean gridiron football, I don't know exactly what you mean (how are the current helmets not "proper"?), but I would say exactly the opposite. The illusion of safety the helmet gives is part of what leads to concussions and CTE.

I'd do away with the helmet entirely. Go bald, or with a simple scrum cap, like in rugby union and rugby league. Techniques will have to adapt somewhat, but that's how all sports have to adapt to technological changes.