Just to clarify, are you using a HubSpot form? Or are you looking to submit non-HubSpot form data into HubSpot?
If it's the latter, you would have to ensure that the form fulfilled the requirements stated on this article: Use non-HubSpot forms.
If you're using a HubSpot form and had like to submit data via the HubSpot form api, you can follow through this documentation: Submit data for a form | Forms API.
As for question 2, when looking to notify user about new form submission, you can add emails on the "Send submission email notifications to" options: