First you have to know that the basic form of 네가 which is 너. 당신 and 너 both mean "you". 당신 is only used when you're angry/fighting, in songs, and in translations when you absolutely need the word "you". It's also used by middle-aged/older couples when adressing each other (just like 여보). 너 is informal. Use it with friends and your little brother/sister. NEVER with people who are older than you (it's okay if it's just a few years' difference). 네가 is 너 + the subject particle -이/가. If you want to know more about this, you can refer to many wonderful explanations just by googling "이/가". The "해" in 사랑해 does not mean "you". The infinitive form of "to love" is 사랑하다. When you conjugate this verb to the present tense, you get 사랑해. So It's basically just saying "love" (as a verb, not as a noun). As you can see, Korean language often omits pronouns as context mostly makes clear who's doing what. If you want to go deeper and break the verb down, it's composed of 사랑 (love, as a noun this time) and 하다 (to do) → to do love → to love. 너의 means "your", it's quite simple when you break it down. 너 (informal you) + 의 (possessive particle). You can attach 의 to any pronoun, name or word to make it possessive. If you add -의 to 나 (I informal), you get 나의 (my). 우리 (we) → 우리의 아들 (our son) 민수 (Minsoo) → 민수의 집 (Minsoo's house) 고양이 (cat) → 고양이의 꼬리 (the cat's tail)

당신 you informal used for significant other 해 does not mean you it means do 너의 is your/s