About why Rumple wanted to know Snowing's child's name: I think he needed to know it because that's how he remembered who he was in Storybrooke: when they were at Granny's B&B in the Pilot and Emma introduces herself, that's when the curse was broken for him (E&A said so in one of the podcast). I think he wrote it in the paper because he want it to be imprinted in his subconscious as much as possible. He might have saved the parchment with the ink "for a rainy day", but that was it.
I agree. He definitely wanted to remember it. But he also made the parchment with the ink in it so that it would aid Emma in the future. He knew she would need it. So, he was basically killing two birds with one stone, imo. :)