Question: So if you collect severance, can you still collect unemployment?
Answer: In Florida, you cannot. They will make you send them a copy of the severance package, so they will know that you got X weeks. Your application will be denied. After X weeks run out, then you can reapply, and you will be approved.
Go to the unemployment office in person to fill out the online application; they have a room full of computers that you can use. When I did this (a year ago), the online application made it look like it failed (I can't remember exactly what the message was), but it actually worked (it was approved), and the employees could tell immediately. Not sure if they have worked out that quirk in the system yet, so save yourself the trouble of wondering and go in person. There is no telephone number that you can call, either; I think you just get a recording.
Many web sites still have the old information that Florida unemployment lasts 12 to 23 weeks. The true number is 12. Not wonderful, but better than nothing.
Hope this helps.