Headscratchers / Lazer Tag Academy

• Jamie gave Tom, Beth, and Nicky their own Starlytes and Star Sensors at the end of the pilot episode, as they also have the power to use them as a time machine. But even though she only knew them for less than a day, she trusted them to not do stuff, as say, travel forward to their eighteenth birthdays in the 1990's and play the winning California Lottery numbers (which would radically alter history)?
• Draxon Drear was retrieved from the Atlantic Ocean, and was taken straight to the Academy, located in Los Angeles. Was there any reason he was not first taken to a hospital on a city on the Atlantic coast?
• Why does Draxon repeatedly try to kill Beth Jaren, who he knows for a fact is his ancestor? This made more sense in the first episode where he was just trying to capture her for the formula she'd eventually invent, but later he was flanderized into just wanting to kill her, even though that makes no sense and would likely cause a time paradox.
  • Especially since Beth is Jamie's great-great-great-great-etc aunt! So if anything were to happen to her, it would only affect Draxon. Jamie would not fade from existance seeing as how she's descended from one of the boys.
  • For that matter, how have most of Draxon's actions not caused a paradox anyway?
• Who would seriously trust something as serious as intergalactic time travel to a 13 year old girl?!?!