If you mean helmets, as in American football helmets, the answer is no. This is because they would simply be too heavy! American footballers can wear them because the game is stop/start and one player doesnt play a full game because they have attacking/defending teams. If you mean a scrum-cap, then yes Rugby players probably should, if they play in the scrum, it will stop their ears from becoming deformed, but many players outside of the scrum wear them too.
Because they are too ashamed to be sitting on the bench
no
Yes, hockey players wear helmets while playing on the ice to protect their heads from potential injuries.
Yes, definitely. lots of ice hockey goalies wear two cups. A regular cup jock and then a special goalie cup over top of that. Usually the size and speed of the puck or ball being shot at the net determines wether a goalie would need to wear a goalie cup. Lacrosse and ice hockey goalies wear cups but soccer goalies generally dont wear a cup
Pro hockey and speed skaters wear helmets but pro figure skaters don't.
Goalies wear the same types of shoe as every other player.
Ice Hockey Goalies do not always wear their team socks under their pads (Practices usually just sweatpants) although for games they mainly do. If you are going to play Ice Hockey, you most definitely need to buy a Goalie Jock. They are padded and usually have thicker plastic for the "jock" part.
About 3 inches thick of padding
people need to wear helmets to protect their heads from the damages
Because they have a death wish. Always wear a helmet. ALWAYS.
Gloves, stick, hockey skates, ordinary underwear, a neck/throat guard, hockey trousers, team sweater
Hockey equipment in the 1960s was not nearly as complete as safe as it is today. Most players did not wear helmets or even mouthguards.