I think I've got this right.
The green tint is typical of a batch of glass containing too much iron oxide. It is usually more visible in thicker finished pieces.
You get rid of it by adding manganese, but, if you add too much, you can turn it purple, instead.
A green tint is often seen in older pieces, too.
This piece was probably cast in a sand mould, with a wet wooden block pushed into the surface of the still-molten glass to create the hollow. I made a few things like this on a weekend course, a few years ago. I suspect it could be a student piece, especially given the quality of the glass.