@NotAPseudonym  
yeah, it feels unnatural, but for some reason, that was all my midnight brain came up with that night.
 
Properly broken down translation will be something like:
 
I want to “(제가) –싶어요”  
empty out “털어놓다”  
my “제”  
concerns “고민을”  
to the princess “공주님께”  
of friendship “우정의”  
whom I’m very fond of (favorite) “제가 제일 좋아하는”
 
“I want to empty out my concerns to the princess of friendship whom I am very fond of.”
 
Better translation would be more in the lines of
 
“I want to tell you about my problems, my favourite princess.”
 
“Out of my system” wasn’t the best phrase to use. ._.

@Background Pony #C048  
제가 제일 좋아하는 우정의 공주님께 제 고민을 털어놓고싶어요  
I’d like to tell my favourite princess of friendship my concerns out of my system.
 
The problem with translations like this (I think) is that while it’s (I assume) completely accurate - it’s very unnatural sounding English, nobody speaks like that.

Edit: Looks like this has it covered better: >>1322805
 
The translation is pretty on point on most parts, but if I may do some refining…
 
Panel 1  
Spike: 트와일라잇! | Twilight!  
Twilight: 왜? 스파이크 | What is it, Spike?  
Spike: 네 앞으로 편지가 와서 | A letter for you arrived
 
Panel 2 and 3  
TS: 누가? | From who?  
S: 안쓰여 있어. 직접 열어봐. | It’s not written on it, try opening it.
 
Panel 4 to 6  
세상에- 스파이크! | Oh my gosh, Spike!  
이건 내 팬레터야! | This is a fan letter!  
나 이런거 처음받이봐. | This is my first time receiving one!
 
손편지라니 귀여워 | It’s hand-written, cute~  
고민이라고도 쓰여있네? | It says they have a concern?
 
Panel 7 to 8 - letter  
안녕하세요, 트와이라잇 공주님  
저는 평소 공구님을 동경하는 ㅠㅗ니빌에 사는 암말입니다.  
Dear Princess Twilight,  
I am a mare living in Ponyville who adores you.
 
 
제가 제일 좋아하는 우정의 공주님께 제 고민을 털어놓고싶어요.  
꼭 만나주세요!  
I’d like to tell my favourite princess of friendship my concerns out of my system.  
Please meet me!
 
Panel 8 and 9 - dialogue  
이 근처일텐데 | It should be somewhere around here  
나에게 털어놓고 싶다는 고민이 뭘까? | What do they want to talk about anyway?
 
Panel 10 (last)  
이런 골목에서 만나자고? | They want to meet in this alley?  
이런 골목은 오고싶지 안지만 | I don’t like this alley,  
내 첫 팬레터 포니를 내칠순 없지 | but I can’t disappoint my first fan-letter pony.
 
This does sound more like a setup as @raw19 mentioned , but I think I’m wrong.

@NotAPseudonym
 
Sounds more like the set-up for a kidnapping. I’m worried yet intrigued.

Let’s see what Google Translate makes of this…  
_{Liberal transliteration ahead - disregard if a real Korean bilingual shows up.}
 
S: Twilight!  
TS: What is it, Spike?  
S: Letter for you.  
TS: What about?  
S: I haven’t opened it.
 
TS: Oh my gosh! Spike, this is a fan letter, my first one ever!  
TS: It’s hand written too, how cute…  
TS: It’s a request for help?
 
‘Dear Princess Twilight,  
I am a mare living in Ponyville and I really like you.  
My favourite princess, I need to meet you to tell you my problem!’
 
TS: Somewhere around here… I wonder what they want to talk about…
 
TS: They want to meet in this alley?  
TS: I don’t like it, but I can’t disappoint my first fan.
 
 
This sounds like the setup for a confession of love, wonder if there’s more?
 
-Oh… well, yes, there’s a next page, and uhm… I had to fix the rating. Upwards.  
Oh well. In for a penny in for a pound…-
 
The next page was correctly tagged, I found the next-but-one page which wasn’t and I’m not translating an entire porn comic in comments.
 
continue?