A lot hinges on whether the OP legally owns the flat, which is a question that hasn't been answered. This means who's name is on the leasehold / land registry documents, and if both names are on there what the separation is, ie by joint tenants or tenants in common.
Presuming the land registry documentation for the OPs flat is soley in their name, then there is no need to consider further.
If the father is a named party, then I would advocate talking to a solicitor - due to the length of time you have been at the property and the investment you have made then you probably have a fair case for Estoppel over the property.
After talking to the solicitor then get the LA to do a financial assessment over your fathers affairs. If you are named on the deeds they may disregard the property (at least your flat) because it would be too onerous to persue, particularly as two properties and a freehold are involved, or they may issue a mandatory (some LAs still list carer as a mandatory disregard, so if you provided care..) or discretional disregard. If you are the sole named party on your flat it won't even be considered.
I would'nt advocate signing up to a DPA, they are basically a loan, with interest, administered by the LA and require the sale of the property (or start of same property) within 90 days of death.
Having dealt professionally with quite a few of these cases where the waters are muddied (ie not just a vacant house), my advice is always, 1/ find out your position 2/ chuck the ball in the LAs court, sign up to nothing and wait for their answer on how they view it.
But, i'll return to the key point, which the OP hasn't answered - whose names appear on the land registry documents, and how are they divided? How is the freehold arranged?