Hello Maja,
... and welcome to our forum.
The only way to set a field read-only is with rules. In your case that you would like to set several fields to read-only after the form is saved I would suggest that you use another (boolean) field and call it for example 'EditMode'. As the default value for this field you can set 'true'. After the save or submit process at which I don´t know how you are doing this you can set the field 'EditMode' to 'false' with an action rule. And then you can set a formatting rule to all of your fields which you want to set 'read-only' after it´s saved --- in this rule you have to check the formatting 'Disable this control' and the condition 'EditMode is equal to false'.
Hope that helps.
Regards,