The Fundamental Problem With 'Orange'

The anime 'Orange' is the shoujo-slash-science-fiction that has taken the summer by storm. We've hit the fifth episode (Out of thirteen) of this anime. But there is something that sticks out in my mind. Something significant.

With the most recent episode (Episode five), we were lectured by the gang's chemistry teacher about parallel worlds and time travel. This brought up a few questions about the story.
But let me explain.
The story revolves around our main character Naho receiving a letter from her supposed 'future self' who has many regrets, mostly about the new kid Kakeru. The letter is a few pages long (As seen in the way Naho holds it like there is more than one.) Within its pages, the Future Naho explains what she regrets...and how to stop it. The Current Naho is supposed to prevent these regrets from happening. And maybe even save Kakeru.
But where did the letter come from?
This is a fundamental question. The whole series revolves around the letters being legitimate (This legitimacy is established early on. Naho discovers that there IS a new kid named Kakeru and some other facts that are from the letter.) 

Here are a few possible explanations.

The first one is the most obvious one. Time travel. The anime hints at it; the teacher talks about parallel worlds and time travel. Episode five is divided into two parts; one is entirely about Naho thinking about parallel worlds and time travel. 

Here is the problem, though. Bear with me. This might get a little complicated. If a letter from Future Naho went into the past to Current Naho, wouldn't this cause a paradox? (Let's quickly define a paradox. According to Merriam-Webster, a paradox is "something that is made up of two opposite things and that seems impossible but is actually true". In layman's terms, that means something that shouldn't exist but does.) In terms of time travel, though, a paradox is a bad thing with a capital B. It's so bad that a paradox would rip the fabric of time. (You might have heard that phrase before. Doc Brown said it in 'Back to the Future'. Not sure which one, though.) 
Simply put, the letter delivered via time travel = paradox = how are they existing?

Of course, if you believe in the parallel worlds theory, the letter caused a change in the future. So the Future Naho (From Future 1) doesn't exist in Future 2. Future 2 is caused by the existence of the letter and Current Naho's actions. So Current Naho caused Future 2. 
Okay, you're probably all confused by now. So here's a little diagram to show what I'm talking about.

Does this make more sense now? But this is, of course, if you believe in that theory. If you don't, then Current Naho's actions could destroy the world. And the letter might not even exist anymore. But that's a topic I'd rather not discuss. It's too big for someone like me. 

If ripping apart time and space with a simple letter isn't satisfying for you, I have another route. But it's awful. It's the only other option I could think of. And that is...the letter is a really elaborate prank. Introduce the letter to Naho and have Kakeru ACT OUT what will happen. Therefore, the actors (Kakeru and whoever else is involved) know EXACTLY what the letter will say and know EXACTLY how to act. 

This is a sad option, though. This means that all the feelings Current Naho has for Kakeru are from a bad place. This means that Kakeru lied to them all. 
And I don't believe that he's the type of person to do that. After all, he acts so kind to everyone. I try to think positively about Kakeru and hope he has a future living. You know, the thing the rest of us do? That. 
I want the future to change. 

So. What are your thoughts? Do you believe it's from time travel? Is time travel even possible?