My understanding is: You have the option to elect to be taxed

either as a non-resident allien, or a resident allien. It is correct that 按照resident報稅就不能免稅了.

So you need to figure out which way saves you money, i.e. is the tax you saved more than the rebate check?

To make changes to already-filed tax return, you need to file amended return. Go to IRS's website and research on the topic.