The answer to both questions is yes.
Yes, you may get your manuscript copyrighted. In current U.S. law, a copyright occurs automatically at the moment of publishing (and Tapas is a publusher), but you may manually submit a document (or a song on CD) to the U.S. Copyright Office with an application. It costs about 30 bucks the last time I looked into it. The purpose of filing would be to make you feel better about it and to a much lesser extent legal documentation. 30 bucks and half an hour of work might be worth it to you for that peace of mind.
Yes, it is not a big deal. As an editor, I have worked with writers who are paranoid about a mysterious someone stealing their story. They won't send a copy to a reviewer because it might get plagiarized. They won't send it to a publisher or a printing company company. They won't send a copy to the copyright office because they don't want it in the public records. They don't want me to read it without offering some proof that I will not do something nefarious -- and they don't know what such proof would look like. When I encounter these writers, I walk away. Let them keep their manuscripts in a locked drawer where no one will ever see it, and everyone will be happier that way.
Meanwhile my wife has written six books, and we've only gotten five people in the world to read them. She would be tickled pink of someone would try to plagerize a story of hers.
When I wrote my Alien Fiction books, I simply released them with a Creative Commons license. Yeah, I'm giving them away. There's still nobody interested in copying my story even with my permission to do it.
I'm not a copyright lawyer, but I play one on tv.meme