Q:

What exactly triggers a row enhance awakening?

The row enhance awakening says it gives a 10% damage boost when you match a row of 6 orbs of its color.

Do the orbs really have to be in a row? What if I match 6 orbs of its color in an L-shape, or in a 2x3 block?
Assuming they don't have to be in a row, does it have to be exactly 6 orbs, or will any match of 6+ orbs work?
What if The whole board is that color so I clear it all in a single match, e.g. by using Raphael then any heartbreaker? Will that trigger row enhances 0 times (since the match was >6 orbs), 1 time (for 1 match), or 5 times (for 5 rows)?

A:

I'll address your questions point-by-point:

The orbs do indeed need to be in a row.  Just having a chunk of 6 orbs together isn't enough, it needs to span the screen from the left side to the right side.
While they do need to form a row, you can match additional orbs with it as well as long as the row itself exists within your match.  It still counts as a row if, for example, you make a giant L shape consisting of the left column and bottom row.  Extra orbs with the row will increase the damage by a slight amount as well.
Clearing the entire board as one color counts as a single row - a giant one with 30 orbs.  Note that this does do a lot more damage than just a single row, about ~3.86 times more in fact.  However, whenever possible you'd want to match multiple rows since that will tend to do more damage (eg. 2 separate rows instead of one clump of 12 orbs).

There's a good in-depth explanation here on the calculations behind how the awakenings contribute to your damage, but the general gist of it is that you'll need at least 3 of them before it becomes advantageous to match rows instead of separate groups of three.

