If I'm in a DMP but still receiving letters and calls from my creditors, what can I do? Can they still take me to court?

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Unlike an IVA, when in a DMP, your creditors always reserve the right to take further action against you, which may include court action. This could only happen if you failed to honour what has been agreed under your DMP programme. Generally we find that as long as you are as reasonable as you can be, creditors will view it as a last resort.
It is important to understand that you will keep receiving letters, calls etc from creditors in the early stages of your DMP. We would ask that you forward all letters to us (if we are handling your DMP) so that we can deal with them for you, and we will provide freepost envelopes so that you can send them to us at our expense. Similarly, any calls you receive from creditors should be directed to our team here.

A Debt management plan is an informal plan. That is to say you do not need an Insolvency practitioner or the leave of the court to enter into an arrangement with your creditors.
Whilst it is informal and some people choose to go it alone I would recommend using a reputable company to manage your 'creditors' and your monthly repayments.
Imagine that you are in dispute with someone and you are unable to resolve the matter to mutual benefit. You may choose to involve a middle man. Now the middle man must remain impartial as he still needs to get the 'other side' to allow you some breathing space. But he is acting on your instructions and looking after your interests.
If someone owes you money and tells you that they cannot pay the monthly amounts agreed, understandably there is a breakdown on trust. The mediator can act to help rebuild this trust and manage your repayments at an affordable level.
Choose your debt management company carefully and you will find the 'noise' dies down after the first 6 months but you have to hold up your end of the bargain and maintain your affordable payment.