If you are using a Microsoft account, you can still log in, even if your Internet is not working. Your password is actually saved on your PC, so Windows can always log you in, even without network access.
I'll answer the second part first: It's not possible for someone to log in to your computer unless you give them permission, whether they're using a MS account or not. Using MS login does not grant the world access to your PC; it simply synchronizes your password with your MS password and automatically updates your password on all of your Windows 8 devices.
As to the first part, the answer is "no, not really." Even if you log in with a local account that's not tied to an MS account, Windows will try to link your account to a Microsoft account when you use the Windows Store or any app that links to an MS account. You can tell each app to ask for your password separately, but Windows will still ask you for each new app.