Yeah I've been through all that for 30+ years. I've registered copyrights, I've registered trademarks and sure they do protect you but copyright is still a given and if you can prove it's your work there isn't anyone in the world that can take that from you.
You also have to take into account that you can't copyright an idea, so the plot of the book is almost impossible to protect, it's the words you protect, therefore copyrighting a partially finished book could see the author only partially protected. Also as a first book it's not going to be great and therefore more than likely not going to have a line of people willing to steal it. And there is already a thousand books out there that use a similar premise, similar plot and are already published, trust me they are out there even for the most obscure genre.
Poor man's copyright may not come with the benefits but in the real world the chances of your work being stolen are pretty damn slim.
Writing under a pseudonym and revealing the real authors name can happen in many ways. It could be as simple as a byline on a cover, it could be so much more. But before any author worries about the name on the cover they need to write the book, edit it, send it to beta readers, edit it again, pay for a line edit, re-read it, pay for a full edit, and then start shipping it to agents if they want traditional publishing. The truth of the world is only a very very very small number of fist time authors get picked up and it's a long process. The publishers wont even give a crap if you call yourself Uncle Fairynuts on the manuscript, if they like it they will give you the pros and cons of choosing names for publication when they offer a contract.
On the self pub route of course it's all different, you buy an ISBN throw the shit on Amazon because you've read it three times and think you can edit it your own work and then another half arsed novel gets released on the world. But the advantage is you can change whatever you like when you like.