Pretty simple do all characters you start get the bonus items from digital delux edition?

You get a few items. You pass them out to whoever you want.
-edit- I just understood your question fully. I don't have the answer for you, sorry.

you get a chest with 4 different items however due to the dum way dLc was added untest it makes another copy of the chest after each patch so yes i have like 5 copies so far

i assume Larian will get their shit together day of these days and make it so you only get the 1 but when that day comes its a safe bet someone will bring out a mod

p.s, yes every time you make a new game the chest should be waiting at your camp