How did Naruto elude the Ninja chasing him at the start of Episode 1?
First of all, he was vandalizing around the town when the two guys were chasing him. He steals the scroll later on. And it wasn't the transformation jutsu either. Just a simple trick with the wall paper. Now don't ask me where did he get that wall paper.

As for speed, even if he is a rookie, he is still a ninja and the other two didn't seem to be exceptionally skilled either. If it's someone like Kakashi, clearly he didn't have a chance.