Regarding computer accounts:
I've had trouble finding any clear documentation about this, so I'll have to answer from my experience. And in my experience, yes, Everyone permissions do apply to computer accounts. (For example, if you grant write access on a share to Everyone, then machine account MYDOMAIN\MYMACHINE$ will thereby get write access to that share.)
Many will find this obvious, but to be explicit about a couple of cases of accessing network resources: Some of the most well-known built-in identities -- e.g. NETWORK SERVICE -- identify as the computer account (eg DOMAIN\MACHINE$) when they access network resources (e.g. network shares). Because computer accounts are in Everyone, we therefore know that processes running under, say, NETWORK SERVICE, are also thus considered as in Everyone for the purpose of accessing network resources. (Theoretically IIS app pool identities should also identity to remote machines as the local computer account, but apparently people are having trouble with this. In contrast, the Local Service account definitely won't count as in Everyone if it accesses resources -- because Local Service identifies to remote servers anonymously, rather than as the machine account.)
(Most of my experimentation involved having Windows Storage Server 2008 as a file server, and trying to access that from Windows Server 2008 (Standard) or Windows 7 Pro. Access from the client machines was made by a process running under NETWORK SERVICE, which authenticates remotely as the client machine's machine account.)