Will the Hammerhead be a practical option for everyday gameplay? Can I hop in with a friend or two and an NPC crew and e.g. go hunting pirates to make a profit?

Like all our ships, it can be manned with a minimal human crew, but the difficulty in doing this may outweigh the returns, depending highly on what missions you undertake. With the given example it would be perfectly possible to achieve that scenario but having a few more friends to help out would yield a more enjoyable experience.