Arena tier bones as well as great hall affects ALL areas of the game.

You mean based on your arena rank? They affect everyone, everywhere. All at once :)

as others said the stat increase from arena battles applies everywhere, you should aim to use all arena medals daily as its one of the biggest long term progressions you can do on ur account, personally i think going for accuracy as some of ur first stat boosts is the best way to go.

You should always wait for a CvC to use arena medals , which is the currency to upgrade the great hall ... only time this gives pts for something and happens every other week .. 

Unless you were talking about arena token...then yes use them all if possible , medals grinding greatly help all your champs .. current and future ones 

ya i worded it wrong my bad, u should indeed save the medals for cvc for big points, but be using ur arena coins daily to get as many medals as you can.