Where the word "Training" appears it's not a "Check". When it's a Check you have to pass it to maintain a qualification. When it's "Recurrent" it is stuff that needs to be repeated at regular intervals. Competency and proficiency are used more or less interchangeably.
"Line oriented" means a more-or-less realistic simulation of a line flight, concentrating on such issues as CRM, Command decisions, "grey-area" rules, etc. rather than the "Handling & Emergencies" type of sim trip.
I'm not going into what you actually have to do as that varies with Operator, Authority, Aircraft type, etc. but you can decode the phrases with the info above.
A batman brings you tea in the morning (or used to...). I never let mine on the aircraft.