WinXP Pro Home Networking

Ok, this is a follow up, simpler question to the one I posted not too long ago, it seems noone has an answer to that one (file sharing is somehow broken).

So, the set up is two PCs, laptop and desktop, networked over with a LinkSys router, no domain, one workgroup ("NETWRK" ). Let's call the laptop ""Lapt" (computer name) and the desktop ""Desk". Both PC's home one non-guest Admin user set up (let's call it "First Second" ) with the same password.

So, First Second is a member of Admin on both machines. The question I have, what happens when I set up a session. Actually, there are several questions:
1) When is the session created? (e.g. if I look in the Computer Management, I see a session with user "FIRST SECOND" open when I access a shared folder from the other PC. The other PC is not showing up by name, but rather as an IP address)
2) The user FIRST SECOND (all caps), does it correspond to the local user First Second and is thus a member of Admin Group, or is it a separate user and thus a member of Users Group?
3) If it is the latter, how come I can not see the user in the Advanced security options when setting up, say NTFS permissions for file sharing (e.g. I would see "LAPT\First Second" on the laptop and "DESK\First Second" on the desktop, but no other users)

Hope somebody can clarify these for me. Thanks.