1. What exactly is a time quake?
I am under the impression that it is an event that breaks the flow between the planes of time. Like when Haruhi first created one and the time travelers cannot travel back to that time because the flow has been broken.
2. Why did Nagato make a deadline for Kyon to gather the "keys"? Why didn't she make the clue easier? I thought she wanted Kyon to make the choice.
This is more of a stylistic choice by the author (and for the sake of time so that the story doesn't go on and on). She did want Kyon to make the choice, but (and this is my opinion) after seeing how he is so passive in the stories beforehand, she made him be proactive for the first real time in the series to choose his true desire.
3. So the Nagato kinda had a glitch with all the stuff she held in, (not to mention endless eight), caused a time quake to erase everything, then she got needled by Kyon who traveled back in time. I thought he was on the hospital bed for 3 days?
Yuki was able to synchronize to see future events to where she goes out of control (likely due to the emotions she's developing for Kyon) so she created a world where the probability of that relationship developing is greater than in the current world. Kyon decides to change the world, but he gets attacked by Asakura and another Kyon actively changes the world back. I won't say any more since the details of this are revealed in a later novel.
4. Do we eventually get to find out who pushed him down the stairs and not manage to physically hurt him? (was it Nagato?) And in the normal world, only Kyon and Nagato know about what really happened right? (until he gathers the group to go back in time to save himself. Wait a minute, seeing a duplicate of yourself can't be good... and I thought Mikuru is not suppose to see the other Mikuru) >.<
All shall be revealed in time. You are thinking along the proper lines, so continue that progression.
5. If the Nagato who caused the time quake stole Haruhi's power somehow, then that means she is really powerful right? Then how come she did not see through the invisible shield she put onto Kyon herself?
She deliberately kept Kyon in his "normal" state compared to the rest of the world. As for why she couldn't do anything else, she states that if she had told anyone else what she would do, it wouldn't have guaranteed that it would happen. After all, it is a "predetermined event". There is no guarantee that what she is saying is the truth.
6. Haruhi > everything? Even the data entity thingy?
As my favorite character would insinuate, Haruhi is like a God. She has the ability to create data from anything as well as some powers the ITDE does not possess, which is why they have interfaces observing her.
7. Also, this is not really related to this volume, but can someone remind me why Haruhi can't learn the truth about her power? How did she get the power?
No one knows what would happen if she found out. It's better currently that she's left out of the loop to keep the status quo. As for how she got the power, it's still a mystery at this time.
8. Why is Kyon a bad nickname? It probably has something to do with his name in Japanese I assume?
Kyon just despises the nickname. It does relate to his real name though.
9. When is the Haruhi movie DVD gonna come out? Any official words yet? I really want to watch it.
Classified Information. Seriously, no one knows but Kadokawa and they are not revealing that yet.
10. I'll let you spoil a tiny bit for me, can someone tell me if Nagato eventually get to have emotions? since Kyon requested it
(personally, I doubt it)
She spent 594/595 years in a loop where she was progressing as a organic lifeform. I wouldn't say that she eventually gets to have emotions, but rather that she's developing emotions already.
I started this post planning to only ask a few questions. More and more questions came to me as I was writing. lol
That's the beauty of thought. When something comes to your mind, more questions will follow.
Thanks you guys!