How do I collect the data from the forms?

Can I import the data into spreadsheets? For example, for a camp registration form, could I filter out the forms for one particular week and input the data into a spreadsheet to create a roster?  Or to find all the campers with allergies?

There are many reports options, you could build an excel report as well and to apply filters to it. Please check related help articles, which I'm linking below: 

How-to-Create-Form-Reports-in-JotForm

How-to-Create-an-Excel-Report

Also, you can integrate form with google sheets: How-to-Integrate-Forms-with-Google-Sheets