The period between the firing and reapplying varies from one facility to another. Some facilities allow you to reapply after 90 days and some after a year.
No, once you choose to get your severance pay, you are not allowed to reapply.
Does quitting without prior notice create a bad impression on my employment history?
Yes, it does create a negative impression on the management and they may charge you a penalty for leaving without formal notice.
