1
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2 This one might be synthetic? There seems to be a bubble like thing inside.
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There are small shiny flakes on this one, hope it is visible
3
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First two pictures are and opal with some fire opal in them. Intersting green color and the fire is the reds. The second set appears to be banded chrystophase though I almost thought it might be a malachite but its to translucent. Third set is unidentifiable as it just looks like a piece of granite or igneous material. Fourth single pic may be from where the first set of opals came from but other than that I dont know. The last is a nice heart shaped bit of quartz with some crystals, jasper and milky chalcedony. My thoughts.
My thoughts, but a hardness test on a few of them would be extremely helpful:
1) some kind of opal, probably fire
2) ocean jasper or a copper silicate but that seems unlikely. DDancer's banded chrysoprase is a possibility. Needs hardness test.
3) Schist/phyllite with decomposed garnet.
4) I'm going with green fluorite. Hardness test as well.
5) I'm leaning toward what DD said as well, but there is a slim possibility of Kona Dolomite. Hardness test would be important.