Point 1 – I think you would be on fairly weak ground since your claimant would, in effect, be having to prove a negative. This is (almost always) impossible. It really depends on what the inference will be but it sounds to me as if you are saying something along the lines of “we were not told about X, Y or Z so there is bound to be even more”
This would, in effect, make it impossible for the claimant to obtain HB/CTB ever again. Course, if you have evidence that there is something else that is a different matter.
It may also be worth writing to your claimant setting out the information you have and asking for express confirmation that there is nothing else. I think this would be reasonable on the LA’s part as would a refusal of benefit if no such confirmation was received.
Point 2 – I think this really depends on property law in Zimbabwe. If, for example, beneficial interest is ALWAYS vested with the registered owner then you have no choice. If not then your claimant clearly has the beneficial interest and I agree you should treat it as your claimant’s capital.