Does GDScript have switch or case statement?
It's yet to be implemented, as you can see here, under Keywords.
Is there any eta for when we can expect to see a Select Case statement for GDScript?
I don't think it's in 2.2 milestone, so it may take a long time.
We won't have switch, as there's already "match" in the current git master branch. So you'll be able to use that in 3.0.
Is it done yet? If not, what alternatives or workarounds could we use?
The GDScript docs have the 'Match' keyword which appears to do the same thing...
A match statement is used to branch execution of a program. It’s the equivalent of the switch statement found in many other languages but offers some additional features.
Yes, but keep in mind that you need the current git version to use it. The next stable version that'll have it will be 3.0 :)