Can an address have negative balance? This address:n1JagbRWBDi6VMvG7HfZmXX74dB9eiHJzU (on testnet) has a negative balance of -0.27388239 according to: https://www.biteasy.com/testnet/addresses/n1JagbRWBDi6VMvG7HfZmXX74dB9eiHJzU, namely, it has sent more coins than it has received. Is that possible? Is it an error on the block explorer?
Short answer: Yes, this is probably a bug in the block explorer.  blockexplorer.com shows a positive balance.

Some of the transactions shown there are "strange" (they presumably have non-standard scripts which someone was experimenting with), and this probably is tripping up the biteasy explorer.

Note that the notion of "balance" of an address only really makes sense when using "standard" transactions, where the output script says: to spend these coins, provide a public key whose hash is the address X, and a signature made by the corresponding private key.  For fancier transactions, "balance" gets more fuzzy.  For instance, I could make a transaction that requires signatures by two private keys, corresponding to addresses X and Y.  Should those coins be "credited" to both addresses, or neither?  Either way the books will not balance.