You can apply for an extension (not an initial in-country visa) until the last day on the current stamp, if you mean you want to get a 30-day tourism extension first.
Then do as Tod says when you apply for a new visa.
Unfortunately, no, you are not safe just with a PDF from the email "[TM.47] (PASSPORT NO : xxx) FORM FOR ALIEN TO NOTIFY OF STAYING LONGER THAN 90 DAYS RECEIVED".
You have to wait to get the result, approved or rejected, OR until just before "7 days after" is up.
If rejected, or still pending, You have to go to your local immigration office to report 90 days in person, but make sure you cancel your pending report.
Seeing your due was 7 May, this is what I would do.
Wait until tomorrow morning and check the status. If still pending, cancel it and head to the immigration office. I wouldn't take a risk for any issue in case the officer counts 7 days starting on the due date (and most likely is the case).