Deleting apple imessages
Once you send an iMessage, if it is completely sent, it will be held indefinitely by Apple (not sure how long indefinitely is) until it is received by the other party. There are occasions where you won't get a "received" notice - if, for example, they have receipts turned off, or if they went out of range after receiving the message (happens on the subway here in NYC, where there is cell service for 300 feet, then nothing until the next station). Even then, it will sometimes send a receipt when it reconnects, but it's not perfect. 

With SMS, it seems to vary by carrier. I've had messages that I know were sent but never received, and there aren't receive receipts for SMS. So YMMV with SMS.

The only time you really know 100% for sure is when you get the received receipt from iMessage. I'm not sure if this helps with your worries.