Could be prehnite and some zeolite. (last pic)
I'd recommend a hardness test on a not so fine specimen, if you got one to sacrifice. Knife and quartz for testing.
I did try scratching glass, and it seemed to ever so slightly mark the glass - nothing like quartz does though. I'll do some more testing tonight.
One question, I have some extra shower tile (I think porcelain) and was wondering if I could use the back side of it for streak testing? Or, is there something special about porcelain for streak testing?
Considering neither prehnite nor chrysoprase/chalcedony has a streak...well a streak test aids no useful info.
But in a general term, yes, as long as the porcelain isn't glazed it's fine.