Very pretty vase! It is a kind of glass called opalino. The fazzolettos can be difficult to attribute. Four companies that I can think of that did a lot with opalino are Fratelli Toso, Seguso, Salviati, and Barovier & Toso. The pontil area looks most like the first two companies, but I do not know for sure. I hope someone else knows something more definite.
Anita