Is it permissible for siblings to give their half-brother a sum of money in exchange for his relinquishment of the father's inheritance, if this is done with the consent of all parties?

If the half-brother is an adult and of sound mind, and an agreement is reached to exclude him from the inheritance in exchange for a known compensation paid to him by the heirs, then there is no harm in that. This is called "al-mukharajah" (release from partnership/claim). It is when the heirs reconcile on excluding some of them from the inheritance in exchange for something known, either from the estate itself or from other sources. This contract is permissible by mutual consent, and its consequence is that the heir acquires ownership of the known compensation, and his ownership of his share in the estate ceases, transferring to the remaining heirs.