1. Would it be easier to Do the Greenleaf trail just to Lafayette (and maybe on to Lincoln) and then back the same way? I get the impression that, once on the ridge, it isn't too tough, but the down via Falling Waters could be tougher that just backtracking (which would also allow for a second rest visit at the hut).
This idea would make the hike much shorter, and miss almost all the good parts. As others have noted, the standard loop is over Old Bridle Path and Falling Waters trails. Greenleaf is an OK trail, not difficult, but nothing special (and annoyingly long at the bottom - the trailhead was moved when the highway was built). You would get good views once you're above the hut, but to get your money's worth from this hike you really need to explore the ridge, which means continuing south at least to Mt Lincoln, and preferably to Little Haystack.
Once on LIttle Haystack, going back over Lincoln and Lafayette is much more effort than heading down Falling Waters. FW is a more direct climb than Greenleaf or OBP, but it's not difficult enough to avoid, even for descent, barring unusual ice or flooding. Backtracking the ridge will be very tempting if you're feeling strong and have plenty of daylight, but you asked what was easier.
As noted by others, the standard loop is OBP-FW, and I, like Tim, prefer to start with FW. This way the steeper trail is climbed, not descended, and the cooling falls are encountered during the effort of climbing. On OBP there are ledges where you can look and see where you've been, nice place to linger near the end of the day. But you can do the loop in either direction, no problem. Note that FW trail crosses the stream repeatedly, so you can start with empty water bottles on that trail too.
2. Are the blackflies as bad as the Dacks?
Highly dependent on date and weather. I have limited experience of the Daks, but I think the Daks are a bit worse on average.
4. Any other similar (or less strenuous) mountain hikes that you would suggest?
If you're going to the effort of traveling, this is *the* classic loop hike. You can get more views for more effort (Presidentials, Bonds), and there are some real gems of smaller peaks (Baldfaces, welch-dickey, monadnock, Cardigan, Chocorua) , but this one is a great balance of accessibility, views, and effort. I'd also mention Moosilauke - lots of loop options and plenty of above-treeline area there.