No 2 first: The 'grant of representation' for dealing with the estate of a person who died intestate is called 'letters of administration', rather than 'probate'. So whoever deals with that estate is an 'administrator'.
There's a 'pecking order' of people who can apply for the grant, with the mother taking priority over the brother. However (as I understand it) the mother can renounce her right to apply. [I used to draft wills for a living but I'm no great expert on the trickier points of intestacy; my job was to prevent such problems arising!].
No. 1: If a will leaves something to someone who has pre-deceased the testator, the terms of the will might cover that situation anyway. (e.g. I leave the sum of £1000 to Fred Bloggs subject to the provision that if the said Fred Bloggs should pre-decease me then I leave the said sum to Battersea Dogs' Home).
If a will doesn't specify what should happen (if a beneficiary under that will pre-deceases the testator) the gift passes in equal shares to the children of the deceased beneficiary (if there are any).
However if the deceased beneficiary didn't have children, the gift 'lapses' and a 'partial intestacy' is created, with the unallocated part of the estate bing distributed in accordance with the intestacy rules.