1) The osier was a type of willow and it had tough pliant branches which once had a variety of uses, especially in basket-work: the word came to be applied more generally to willows and to the branches themselves.
‘Osier hope’ is a rare term, recorded in the OED under ‘hope’: 1607 I have planted an Ozier hope … in a surrounded ground, fit before for no vse, for the too much moisture and overflowing of it. It was said to be a word found also in Essex and can be compared with osier holt and osier bed. Two Yorkshire examples are from roughly the same period: 1615 lez Eightes, Les Osier hopes, vineyards, willow trees, Lez wares, mildames & Fludgates, Almondbury
1623 all messuages … eightes, les osiers, hopps, fishwandes, sallowes, the weares, mildames, rundells, Butterwick. I believe the punctuation in this transcribed indenture masks the second example of ‘osier hope’, and since ‘eightes’ were aits or small islands it seems clear that willows were being coppiced in enclosed, marshy areas by the river or possibly on small islands. Halliwell described ‘ait’ as a little island where osiers grow. Objects made with osiers are on record from the same period: 1621 Two little osier baskettes and one greater, Slaidburn.