hi Monica - welcome to the GMB

A most unusual shape - how does it stay upright?

The signature looks to have been created by the use of possibly something like a Dremel, using a stylus point, or perhaps just a stylus without the Dremel - but not what I'd think of as etching, which is a wet acid process. Signatures are very often created using a steel stylus point.
Nice pictures by the way - of someone's lawn and fence post - unfortunately, these are a distraction and combined with light reflections are making it difficult to see the wording, so not possible, for me, to see these clearly enough to comment.
If you are able to re-take your pix of the signature - with a plain darkish background and with light falling onto the signature then this might help - it might also help to rub either some carbon paper black, or talc powder, into the words.
Your piece doesn't make me think Scandinavian, so perhaps either the States or possibly European, but famous last words as they say - if the seven doesn't have a cross bar then probably not Continental.
Glass travels - more so than you'd ever imagine - so could be from almost anywhere. From where did you acquire this piece?

Sorry, not a particularly great day here - lots of rain, dark clouds, I'm older than I'd like to be, and could do with more money - but apart from these minor niggling details, then passable I suppose.

Look forward to seeing some more pix.