Will I be allowed to reapply for a mathematics NSF postdoc next year after declining one this year?
If you accept another position before the NSF Mathematical Sciences Postdoctoral Research Fellowships are awarded, you should officially withdraw your NSF application.  The way the NSF postdocs work is that there is no second round of offers: if you are awarded one and turn it down, then it won't be offered to their next choice of candidate, who might have received it if you had withdrawn your application.  Furthermore, I believe withdrawing will preserve your eligibility for next year, while you will not be eligible if you decline an offer (according to the official instructions).