Am I able to insert the applcation form I created into our Association website and have applicants submit the completed form to the designated folder?

Hi there,

Am I able to insert the application form I created into our Association website 

Yes, you can embed your form on your website. Here's a guide to help you - Embedding-a-Form-to-a-Web-Page 

and have applicants submit the completed form to the designated folder?

You can integrate your form to Google Drive so when someone submits to your form, it will instantly send uploaded files and the data on the forms to your Google Drive folder.

Guide: How-to-Integrate-a-Form-with-Google-Drive 

Hope I have answered your queries.

If you need further assistance, please let us know.