Does BitMinter support the new(ish) AsicMiner Cube out-of-the-box?
No. I've been told they work the same way blades do. So you connect them through a Stratum proxy (Slush's Stratum proxy, or bfgminer which can also work as a proxy).
What's going on today? the site is offline, is it being DDOSd?
Is the mining still taking place? or should I go for a backup pool?
Website had a short hickup. Sorry about that.
If mining is working, then there is no need to worry. The mining server will kick you out if things go wrong.