1) 24 didn't disappoint.
2) It's entirely possible that the EHIC website was only down temporarily, or it might not be accessibe from work. Either way, I was able to apply from my home PC (in the brief spell when my broadband connection was actually working right).
3) My broadband connection at home is back, but it's currently slow, erratic, and prone to kicking me out of MSN in the middle of a sentence. My ISP have given no indication of when these problems will be resolved, and have not replied at all to the email I sent asking this. I'm not best pleased with them, despite being very glad that I'm back online.