other people's voting paperwork

Same way as they would for the ID, They don't. That's not a common problem. Only people in the same household could possibly access the paperwork and as there are only 250-ish people voting at the same polling station, risk is high that someone voting twice with paperwork of a family member would immediately be found. That there are enough cases of this to sway election results is highly unlikely.

voting several times

Check list. Everyone that is registered at that polling station is ticked off on the list.