How can I check when my next rent payment is due?

Any upcoming payments due shortly are displayed on your dashboard page, under "Payment reminders":

To see a full breakdown of all future payments due, click through to your account - which you can do by clicking on the "Balance Due" figure on your dashboard, or by clicking through to your current tenancy and then clicking "Account".  The account page shows everything you are due to pay over the course of your tenancy, ordered by date.  Future payments due are at the top in a lighter colour.