Is it permissible to cut the hair completely with scissors after 'Umrah or Hajj, or must it be shaved with a machine or razor? And must I leave the sheep I bought for the fidyah to my children in Egypt for them to slaughter on Eid, given my intention to perform Hajj this year?

The best action after Hajj or Umrah (definition) is to shave the entire head. If you intended to sacrifice a sheep (as Udhiyah (definition)) but did not verbalize the intention, it does not become an Udhiyah merely by intention according to the Shafi'is, Hanbalis, and Malikis, and you are permitted to dispose of it as you wish. However, if you verbalized that it is an Udhiyah, then it must be slaughtered according to the Hanbalis, Shafi'is, in addition to the Hanafis. If you only intended to sacrifice it, it is best to slaughter it to avoid scholarly dispute, and because Udhiyah is a Sunnah (definition) for the pilgrim.