No gave up Twitter because it was ****e! and mainly on PC, but I did use it on my titan briefly with no problems, Don't know of anyone with similar issues sorry, Is it a branded O2 handset? I have an unlocked lumia but not sure where it originated/carrier wise as was from ebay, I would bitch slap the counter staff and get either a working one there and then or tell them to replace it with a 900, Really cannot think of why you cannot open links?
Read a few reviews of the twitter app and peeps complaining about not being able to log in etc, Maybe it's a lumia thing?
Or even a Giff gaff problem that is assuming ur still using your sim?
Try a different sim or even wi fi alone to narrow down your options.