Here's your review, finally! I hope it's helpful, and good luck in the competition!
-Paragraph one, you say, "...before moving on to prepare his own." His own what? Transport? I'm not even sure what a transport is at this point, so it makes it hard to visualize what he's doing to prepare it.
-"She gave a long drawn out sigh, swept her eyes around the room once more, and walked out." You need that comma after "more".
-"Taking a hesitant step out of the house, she..." It's generally a good idea to use the character's name in the beginning of a paragraph, then switch to the pronoun after.
-In the same paragraph, make the semi colons into commas and add an "and" before the "the empty blue sky relaxed her..." Semicolons are only used when you're joining two full sentences that are very closely related, but could stand alone.
-You missed a period after "replied" in the line that begins, "Just...not..." And after "snorted" in the line after it.
-In the line that begins with "Fine...", you have "headquarter" rather than "headquarters."
-In chapter two, "more-than-happy" doesn't need dashes.
-I don't understand the line, "Well, I think you need to take a better look." A better look at what? At the girls? At himself, his attitude towards them?
-Why does the teacher call him "Max"? I thought his name was Henry Harrison. -You cleared the confusing comment up a bit, but I think my point still stands. I was still confused.
All things considered, you're off to a pretty good start! I like the premise of going back in time, and it's obvious that this girl is very important in the future. The main criticism I have plot wise is the fact that you haven't returned to this subject. I know it's only a few chapters in, but by the end of the third chapter, I'm a little afraid that it's heading down a path where the story becomes more focused on their every day life than on the time thing. When you start a story out with something as intriguing as that, be sure to carry some thread through which keeps the reader interested and makes them remember why they started reading in the first place. But it's good, though, do keep going! Good luck!