This month, my pension goes into my bank account on the same day that the Standing Order, goes out for my rent.
Do these two transactions take place during the early hours of the day in question. If they do, then I don't have to make a deposit to cover a yearly insurance premium, due to go out the day before.
You can change the date of a standing order for your rent (compared to DDs where the recipient has to agree to the change) so i would just see if there is time to put the date of the SO back by a day or two just to be safe. You can do it easily online if you have online banking
Not a problem, anything going in or out on the day using BACS are processed by Start of Business and would be taken into account before you would be able to carry out any manual transactions