All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If the heirs are only those mentioned in the question, and the deceased did not leave any other heir, then the inheritance should be divided between the two full-brothers and the full-sisters by Ta’seeb (by virtue of having a paternal relation with the deceased and not having an allotted share, so they get what is left after the allotted shares have been distributed); the male twice the share of the female as Allah Says (what means): {If there are both brothers and sisters, the male will have the share of two females.} [Quran 4:176]
However, the two sons of the full-brother do not get anything from the inheritance because they are prevented by the existence of the full-brother.
Therefore, the inheritance should be divided into 7 shares; each full-brother gets 2 shares, and each full-sister gets 1 share.
We apologize for not answering what you mentioned in the notes, i.e. in the additional information, because it is not possible to issue a Fatwa on such matters of dispute except after knowing the reality of the matter and hearing from all the parties; this is of course something that is not possible for us.
What we can say in brief is that if your uncle wanted to gift you something from his property, then one has to look at his condition whether or not he was in his disease due which he was feared to die. If so, then if the gift was possessed by you [the person to whom it was gifted], then it is effective within one-third of his wealth only, because it takes the ruling of a will; the same thing applies if he wanted to make a will to you after his death and did not intend a gift.
In case he was not in his disease due to which he was feared to die, then he could have gifted you whatever he wanted from his property, and if you possessed it when he was still alive, then the gift was valid and none of his brothers or sisters can object to it.
Hence, we advise you to orally ask those questions to the scholars so that they can provide you with an appropriate answer.
Allah knows best.