5th Musing: Out of Musings (but somehow we get to sci-fi)

So I sorta skipped a day of musings and with my sincerest apologies, I must also say that I have no musings at the moment! But then I thought: Ah! What a paradox this is!
Because really, I am musing about the fact that I have no musings. If I had musings, I could muse, but if I had none then I could muse about how I could not muse.
And that is how this post has the word muse (or a word in its family) 9 times in 5 lines. That should be some sort of record.
But while we are on this topic of paradoxes, I must say they, especially those of the temporal sort, are some of my favorite things about which to theorize. It's because I watch things like Doctor Who and the Melancholy of Haruhi Suzumiya (you can't forget Final Fantasy VIII in addition to that).
I warn you there are spoilers ahead!!

With Doctor Who we could talk all day about paradoxes, so I'll just talk about MoHS. So in the Disappearance of Haruhi Suzumiya (like I said: spoilers coming up). The main character's just minding his own business, trying to turn the world back to its original way and then the crazy girl who we thought disappeared like 15 episodes back randomly comes in and stabs him in the back (literally). So while he's writhing in pain and she's making sure he doesn't make it out alive, two saviours step in and save him. One of them is obviously the main character from the future with his friend, a time-traveler, though they only reveal his silhouette and voice. After the second time watching (and reading a couple of forum posts), I realized that he was only alive at the end because his future self saved him. But how did that future self get out alive?  Technically that future self shouldn't have existed.
Or what about that story where this man wanted to see how a building burned down so he went back in time into that building and knocked down the lantern that started the fire. So basically, he caused what he wanted to witness.
So I have to wonder: if time travel is possible (and I really do believe it is, we just haven't achieved the means yet), could these ever happen?
And what about time loops? How many times have you lived this day if it turns back so that you can't remember? In the Endless Eight (MoHS again), they all felt a strong sense of deja vu. Now whenever I feel that, I get creeped out because I think of time loops.
I'd like to find out how much of this is possible and how to achieve something like this because, really, I believe that manipulating time is a possibility, we're just not advanced enough.