can my internet bill be a dedication for school

No, at least not the whole bill.  You may be able to justify a portion of the bill as an education expense, but it would be difficult to determine what percent of the bill is used as an education expense and what percent is used for any other purpose.  There would need to be a way to document the percentages.

No, if you are using the same internet you had before enrolling in school. If you got new inet or upgraded for school, then the additional charge would be a qualified educational expense.