On the top of the page it says Notifications (on the same line where you would sign out) If you have a PM it will say notification 1,2,3 etc depending on the number of messages you have
If you get a reply from who you sent it to, they opened it. If you don't get a reply, maybe they opened it, maybe they didn't. As far as the TMF message system reliability of it going where it needs to go without a glitch, that's 99.99%.
You can look at their profile and see if they've been on since you sent the message. If they have, they probably read your message and decided to ignore you. It happens. Even when they say they want people to message them, they really don't and ignore you. 😛. It'll be okay though... 🙂