Can anyone tell me when Slingbox 350 will be available in Ireland and the UK?
No one here will tell you. But there is nothing stopping you importing one. Or get a friend who is visiting the USA to pick up one for you.
I've been told that european versions are slightly different to the USA version?
As you said, there is no Eurpoean version so I don't see what you mean. The European Pro-HD is different to the USA Pro-HD as it has a PAL tuner rather than an ATSC one. But the 350 doesn't have a tuner.