I would stay away from the paperless check thing. It causes you to not look at hours earned, thus your blinded to the 5, 10 minutes they might cut from you and having not known the better. I get a real check, worth something, and bring it to the bank myself.
Secondly, its common to send the lower guys home first. But there will be a time when you get a lot of hours as PT. As for being sent home, get the number for the call out place in your building. State your name, where your working and ask if I can work today without being sent home. Call about an hour before start times, someone might just need you due to call ins. This will save you the gas and time from point a to b.
As for the check, go in and see if you have a check there and ready in your name. Your process into paperless might have not gone through the system, or it might never. I tried twice to have mine go paperless, and they both failed. Its not uncommon, HR has too much to do like the rest of us and paperless gets pushed to the very back of the to do list. There might be a real check at the building without a void on it thats worth it. Take a visit there anytime, someone is always around during the weekday, FT or management.