If the only operation you are working with is addition you don't need to. However, if dealing with a long list of numbers, it may be useful to regroup into tens and hundreds and other "round numbers" that you can sum together quickly at the end.
For example 12 + 26 + 88 + 74
= 12 + 88 + 26 + 74 = (12 + 88) + (26 + 74) = 100 + 100 = 200
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No
If the total in any column exceeds nine, you will have to regroup.
Yes.
Yes.
Regroup was created in 2006.