Is it possible to share access to forms and submissions to another user?

Is there a way to share the access to completed forms to another user?  Also, is there a way to allow another user access to edit a form?

Yes, there are currently two methods to share forms and submissions, the first one will allow you to share the builder link so the user can edit the form, and the sub-users method will allow you to share the form and allow to edit and view submissions too. 

Here are the guides:  

Understanding-Form-Collaboration

How-to-Share-Forms-with-a-Sub-Account-User

I hope this helps.