Hello. My name is ***** ***** I will try help you with this.
Your first question is the one you really need to focus on.
If the dpf is nearing saturation point then it requires urgent regeneration.
If it doesn't get/do this soon then it can be very expensive.
Because the dpf is a filter, failure due to saturation is not considered a fault and can be expensive to replace/repair.
What you could try is an automatic regeneration. You need to drive the car on a motorway where you can maintain a constant speed of 60mph for at least 15 miles.
If you cant do this then your local Peugeot dealer can carry out an enforced regeneration with their scan tool.
Hopefully it wont be too late and the filter will regenerate ok.
For the tyre pressure fault, you will need to have the tyre pressure monitoring system checked.
This could be caused by either a slow puncture or a faulty tyre pressure sensor.
The sensors are located inside the wheel/tyre and require specialist tools to check/replace.