For your first post, I have not used molasses to bottle prime but have used brown sugar to prime several styles of beer. I don't think that there is an appreciable flavor contribution in my experience, but it's certainly worth giving it a shot, especially if you have excess brown sugar.
In regards to your second post, I regularly use
Northern Brewer's priming sugar calculator and I notice that it has an entry for molasses that changes with desired C02 volumes. While I don't use molasses, I do bottle prime with honey from a squeeze bottle now. Before filling with beer, I place an empty beer bottle on a scale, zero out, and then measure in grams the honey until I hit my target mass. As a suggestion, you could try a similar process by dripping some molasses in from a teaspoon or perhaps using a kid's medicine syringe until you get your desired amount and, if looking to dilute, you could then add a very small amount of hot, sterile water to the bottle and swirl it around. For reference, I have not had to dilute honey ever but that certainly may not apply to molasses.
Best of luck.