Hi
I will try to write one by one;

First of all having dual nationality seems an opprtunity from my perspective but varies to every individual. So it is up to you, wether to devide keeping Turkish nationality or give it up. But keep in your mind that *regardless what people say* even you would only go for holidays with British citizenship, having a local nationality(Turkish) will help you in many practical official cases. Such as owning a property for holidays, having a second address, or even some legal issues of heritance etc..

Legally for your partner , it is possible to delay untill age of 38 and you should follow it through the Turkish Consulate in London.

If there are some problems occuring with the ID number of him, possibly, but not officially; the guys in the consulate are regular working people and sometimes they are not bothered to deal with problematic issues. That is the address that you can contact and handle all issues whilst you are in the UK... If it seems that they are lack of helping you, about the proof of the nationality; then I advise you/your partner to check out the nationality records of his father. I do not know if his father have registered him to Turkish Citizenship, but e should have done it; as I understand he has an old type ID card (Nüfus Cüzdanı). Turkish Consulate is in charge and OBLIGED to renew the ID cards of Turkish Citizens who are in abroad....

If there is something wrong, then ask the guys in the Consulate to provide an official proof of citizenship either himself or his father (they usually request the records from Turkey, called "Nüfus Kayıt Örneği" or some sort of official registry from the governmental body in Turkey, if they do it it may take quite a long time. Mostly people request it by their self/or friends, relatives etc in Turkey, which makes the process quicker)

But main issue is that they have to match UK documents and official documents from Turkey and clarify the citizenship.

Also I may misunderstand one point; Turkish consulate is working through appointments for many requests, but you can also pop-in directly; or call in order to get an answers for the procedure to follow. My advice is to call directly and get action according to what they say...

This process may seem lots of red tape, but mainly all countries' consulates suffer to help officially in similar situations; even if you loose your British passport in abroad, the British Consulate would treat like a fraudster... this is what experience say...

Anyway it seems that somehow you can clarify it properly, but as I said it will take some time and some efforts. It is completely up to you wehather to follow it o not.

Also about the health issues and the national service; there are some sort of regulations that prevent people with permenant health problems to go to military. And in this case, certain people will be exempted completely from national service. Once a friend of mine did his health check in a UK hospital and they accepted at that time; but it was by his chance. Probably they may ask the health check to be done in a Turkish governmental or military hospital...

LAst advise is that because, (what I understand) he never checked for national service from the consulate, probably he would be in "kaçak". After clarifying the citizenship papers , first thing to do is to confirm this from the consulate and do the necessary paperwork in order to defer it at the moment. Afterwards, the "dövizli askerlik" or any other health confirmation is the next stage...