I thought you might like to see the recipe for the chutney, link is below. I first had it at the Ponti Grill in Seattle, which is out of business now unfortunately. My favorite use is to serve with pan fried halibut, but it would be good with a lot of things. You can make it ahead of time and reheat to serve.
It’s kind of syrupy sweet-tart. I use it as an ingredient in a balsamic mustard vinaigrette.
In addition to the excellent lemon zest suggestion, you could try lime zest.
A local spice that is good for this kind of thing - more the bitter than the tart part - is dried satsuma peel powder, you could find something similar at Chinese food places as well - mandarin peel, called chenpi.
As an ingredient, yes. By itself, I’d say no, it’s a bit overwhelming a flavour. Better to cut it with a light oil or similar.
As long as the pomegranate police don’t catch you! 
Seriously, I think it’s too strong for that. Maybe a bit in the olive oil that you’re dipping your bread into?
Emphasis on the tart– not much like regular sugar cane molasses.
Or use just a dash-- the way you would balsamic vinegar. Actually, upon reflection, I think balsamic vinegar is sweeter than pomegranate molasses.
Which brings me to a simple and YUMMY salad dressing:
equal parts balsamic vinegar and toasted walnut oil. Delish! When I say “equal parts,” I mean maybe a tablespoon of each, not a cup of each. Toss the salad with the walnut oil (TOASTED) and then sprinkle on the vinegar. Insanely great combination.
I must admit, I usually do the “drops of balsamic in a plate of EVOO” thing. It looks so pretty…
Definitely. Or at least, with the good Turkish nar ekşisi, where the tartness is fundamental, vs a really good aged balsamic where the sweetness has really come to the fore. But on the other hand, the cheaper molasses can be so sickly-sweet they might as well be grenadine.
Hmmm… maybe you could generate supplemental income by predicting the future and such. Like reading tea leaves. 
Call it EV-WOO-WOO.