Probably and officially, to maintain the certification, you would need to change to whole lot, but.......

For me, in practice I would assess how risk critical the door is.  E.g. If the door was protecting an overheight single starcase , or sleeping accomodation to high risk/vunerable occupants, or was part of a progressive horizontal evacuation compartment, or was part of an engineered solution- it would be worth considering a complete doorset change

But an office, a cross corridor fire door, or other moderate risk application, I would chage to door only 

Consider a hotel with 300 bedrooms: The bedroom doors get a lots of damage from suitcases, as do doors to stairs and lifts. Then there are doors in service areas and goods lifts. It would almost be a full time job (and full time disruption) change doors & frames!!!

Are you condident the fire door set was initially installed by a certified fire door set installer.  There are such people who attend training and learn about all the correct ancilliary products to use (wood filler etc.).

I'm sure you could source a fire door to fit the existing frame etc. but if in doubt do the lot.  That's my opinion.

You can change the fire door slab as long as it is exactly the same slab as what has been tested.you will need to check the fire door test evidence/global assessment.

In light of grenfell my suggestion would be to employ a Qmark or certifire accredited fire door maintenance company who will source and replace the slab but also give you a sign off certificate to show compliance.

Hope this helps