Did you mention to customer support when you start to travel? That is the main criterion they use to prioritise requests. It is not enough to say your problem is urgent, since people have very different opinions about what that means.

A refund should be executed immediately if you do that via the website. But if it costs money (normally 15%), I wouldn't do that.

The most important question is IMO: did you enter your birth date correctly? If yes, then customer support should handle it. If no, you can request an exchange, see this page.

Yes I did I mentioned I start travel in 1 week, I am scared they will not get back to me in time. Because of the wrong date of birth I cannot book seat reservations meaning I cannot start my journey. I have Eurail Plus which means that I get an 100% refund, if the refund is processed immediately I will refund and get a new pass but is this really the case? Have seen it takes up to 4 weeks to refund. 

You can book reservations now if you want. It's nonsense you should have to wait until the details have been corrected; your birthday is not mentioned on most reservations, with the exception of Italy, in which case booking via ÖBB is cheaper anyway. Most reservations can be done cheaper elsewhere by the way, e.g via DB, SNCF, ÖBB etc.

If you have Plus, then you can just request a refund without a problem of course.

A refund should be really fast if you request it via Refunds and Exchanges. I received mine on the same day it had been executed, although I must say that refund was done manually be customer support.