You need to refresh your password periodically - normally if you've been inactive for about an hour - though it doesn't completely log you out, for example you'll still see the User and Admin menu, but you'll be asked to confirm your password if you try to access those pages. If you are constantly using the site you will not be required to refresh the password.

This happens regardless of whether you tick Remember Me or not.

If you don't tick Remember Me then it completely forgets who you are at the end of the session (i.e., when you close the browser window).

Perhaps the "about an hour" isn't long enough, and it should wait longer before requiring a password confirmation. Perhaps two hours would be better? (or, at least guarantee that it really is always an hour?)

As for the admin options, these should always appear if you're logged in, though the way they look depends on the theme. In Fresh/Clarity you see the new-style Admin menu with a cog button, though in Modern you should see an admin bar at the bottom, and in Bootstrap you can configure where the admin bar appears.

If for some reason you don't see the menu, just add /admin/ to the end of you site's URL and you'll go straight to the admin pages (and you'll be asked to log in first if necessary)

Thanks

Joe