Q1: you can switch to a read-only view on open if the form is not in the initiated state. To check initiated you can use user roles or qRules IsNew, or just use a value in your main data source that you set on submit. The other option is to use a workflow or Web service to move the form to another folder that the user doesn't have access to - hence they can't open and edit.
Q2: use Submit to save. Seriously, if you are using browser-enavbled forms, I'd look at using submit to save. You'll have to Clear Errors if you have required fields - see qRules for that. If you have no required fields in your form you should be able to submit a form. Just label the button save. You can create a Submit button that also submits but with an added rule of setting status to submitted.