1. I'm guessing you want to add a new record for the next customer. In your relation table click on [=] like you were going to modify your relationship. At the bottom click "Allow creation of records via this relationship."
2. The delete button would just delete the current record. If your payments are in a portal you would use delete portal row to delete the one record.
And what tables, fields and relationships have you defined in your database file? Describing layouts doesn't tell us that.
You can delete the contents of one or more fields without deleting the record. This can be done manually by putting the cursor in a field and pressing delete and also with a script that uses one of several different steps that can clear the field.
But you can also keep that data and start a new record, perform a find to find different records or change a portal filter or the value of a match field to make records (and their data) appear and disappear from a layout without deleting any data.