Positive psychology is great! I've listened to the online lecture by the Harvard lecturer, Tal Ben Shahar. If you are interested, maybe we can talk about that?

The first with comma, 100% correct and it fits the requirement for academic English convention. (If you are taking any ACT/SAT test, you have to follow such rules to get a high score.) Why comma? Because “in your letter” is already an adverbial phrase, and after it goes the main sentence, so main sentence needs to be separate to avoid confusion or ambiguity. The second one without is all right in spoken or informal writing.

You are asking the basic question of forming NP (noun phrase) in English. Actually, there may be more than two ways to for NP, yet I won't go that far. 1. NP--> adj+N. the focus here is the latter noun, and the adj. before it MODIFIES the feature/character of the N. 2. NP--> N1+N2 the focus is for N2, and the N1 identifies the origin/source of the N2. e.g. silk shirt, book store. Specially, for this case, there mostly are "settled" phrases, like "hot dog" (as the fast food) v.s. "hot dog" (as a dog that is hot). 3.NP--> N1 + of N2 the focus is the N1, and the of N2 signifies the possessor of N1. And this is for nouns of non-living things, like the map of the World, the wall of the classroom, the virtue of honesty. Specifically, when the nouns are living things, we use apostrophe (') to indicate possessor, like The horse's tail, Jim's sister or metaphorically, today's news. Above are the linguistic reasons for your questions if you do want to know why and how thoroughly. Yet it is as simple to fit the rules next time and as the more you learn, the better you understand.

源 yuán ①水流起头的地方：河～│泉～│发～│～远流长│饮水思～。 ②来源：货～│资～│病～。 ③（Yuán）姓。 The collocations you presented may be correct, grammatically; but not pragmatically...c'z they sound weird to native speakers, like me. 源can be collocated with substatiated things, as the above examples, and unsubstatiated objects, like, 电源， 根源，your 痛苦源（though 痛苦的源头is better）. I suggest you doing some basic readings on Modern Chinese morphology to figure out the rules for Chinese phrase and it will be much easier to learn plenty of phrases after you know the single character! For example, 源泉 and 泉源 are almost different things though the characters are the same.