Sounds like you should be fine. The sample wasn't going to be done testing by thursday. HR didn't know what they were talking about. They should have the test results today. The background check can take a while depending on who's doing it. Have seen them take a couple weeks. I wouldn't worry. I would call HR sometime this week and see if you have a start date yet. Don't ask anything about the drug test.
For ruture reference when the temp is too low in the collection cup, take your thumb and rub it against your clothes for a few seconds and then hold it against the temp strip on the collection cup. When it says 98 hand it to the tech.