Thanks. They blow up nicely!
Your marks are a bit lost under all the wear, aren't they?
One trick to bring them up, is to rub a little talcum powder over it with the ball of your thumb.
That might help (or not!) to make out what is mark and what is scratch, seen more easily.
The vase itself looks perfectly right.
Orrefors numbers are well documented. I'm sure somebody will know what it is, once we know what, exactly, is there.
Ivo Hannstra produced a really good little booklet; "Glass Fact File A-Z", which has most of them in. I do have a copy. (it requires special close-up-focus glasses and a magnifying glasse for me to try to read it.

)