So there's no mining with NXT. Who keeps the computer making transactions online, and why ? How are the transactions processed ? And I understand they are much faster than bitcoin ?
Who and why: Everyone who wants to support the network, or to get some transaction fees (the block generator gets all fees)
Transactions: The forger that generates the block includes the transactions and signs the block. Forgers are chosen basen on the Nxt Proof of Stake algorithm (chances to forge a block a proportional to the effective stake in your account)
Block time is 1min, compared to 10min of bitcoin. Some devs are coding "Instant transactions" as we speak.