Well, the timeline for this fic was altered a bit, Voldemort just challenged the Potters a bit later than canon is all, a year later instead of the usual fifteen months.  I tweaked it that way because I wanted to give Harry and Severus more time with each other when Harry was little to develop a greater bond with each other. 

As for the broom, the spell that shattered Harry's magic did not work as well as it was intended to, his core was damaged, but it began to mend itself gradually, so Harry can fly a month and a few days afterwards, though that is pretty much all he can do. 

lastly, Severus wanted Harry to still study his subjects so he wouldn't feel as though he had to abandon the magical world completely and give up being a wizard.  He hoped that Harry's magic would return soon, sooner than predicted, and in order to give the child hope, he told him to do his summer homework, acting as if it were a normal summer, where he would be expected to complete assignments and wouldn't be allowed to use magic.  That is also why Harry didn't really react too much after awhile, for he was used to doing without his magic over the summer, and he was kept occupied with his new family and friends, so the loss didn't hurt quite as bad.

Thanks for reviewing and hopefully I cleared up those few points.