How do I search multiple fillable forms by using the standardized data in the fields

If the forms all contain the same fields, you can use Acrobat to export the form data from a collection of filled-in PDFs to a data file that you can open in a spreadsheet and analyze the data however you want. This is the easiest and simplest approach. Exactly how you do this depends on which version of Acrobat you're using.

There are things you can do with scripting in Acrobat as well, but it's harder to do and explain.