They are pretty tough
I think the root survives as long as the transplant soil isn't too far off from what was occupying
I will say if you want berries this year or next year or the year after start with a larger plant with year or two year old shoots.
Yep, you got it
Rasberry(blackberry, Logan berry, marionberry, chesterberry, etc...) is 100% a bi-annual cane, fruit second year then that cane dies...rinse/repeat...the yearly growth won't bear fruit first year, second year will be all berries...so you cut them a few months after producing their berries, they will die off afterwards
Blueberry cane can produce berries for many many years though, don't cut them after the second year fruiting, as they have much life left in them...my current bushes are 15 + years old and some canes may be 10+ years old and producing heavy