both the new record and the changes to existing records) persist?
Yes, both the new and edited records will be persisted.
Is there a way I can prevent them from editing other records while in an add and yet still enable them to edit multiple records?
This would depend entirely upon the grid and really has nothing to do with StrataFrame. One thing that you could always do is cycle through the BO and reject any changes for rows that have been "Modified" but leave any rows that have been added. But this could be confusing to your end user and your would more than likely want to make existing records "read-only" within the grid and only allow new rows to be added.
Is it also safe to assume that the user only needs to click on new ONCE and can add multiple records?
The BO will handle as many new rows as you add...as for the interaction within the grid, again this depends entirely upon how you program and setup the logic within the grid.