If it is just me using the computer should those boxes be checked?
Andee, "Enable Guest Browsing" just allows other users, if there are any, to use your browser to browse the Internet without giving them the capability to view your settings, info, auto fill information etc. It can come in handy when you have a friend/guest that needs to use your computer to browse. This mode will also restrict access to what settings they can change and more importantly, they will be unable to change your settings unless you give them admin access.
And if not and it has 'One Person Current' above those two selections... If I delete that will that affect my information?
This just tells you that there is one user signed in, which is you, that is browsing the Internet. That's the way I read it.
'Let anyone add a person to Chrome'
This one, I'd leave unchecked, for sure, because i'm uncertain if leaving this checked will give any user the ability to change your settings.
HTH!