I hope I can understand everything you said here but renaming menu items is done from the menu links which lets you edit the “labels’ of any menu link. As for the home page, blog, etc., there’s two ways:
1. static front page where you make a new home and a blog page, then on Settings >> Reading, you set which is your front page and what is your blog page.
2. Make sure you have a custom menu made so you can drag the pages and other things on to it, such as the home and blog pages
3. You cannot set the page template for the blog like a standard page. It will ignore it. Only way to get a different layout is if the theme supports that option. Encounters does not have a “blog layout” option that gives you three columns. Three column layouts are for standard pages only.