For the most part, every Unix-based and Unix-like (and by extension, Linux) distribution will have a root account (equivalent to a system administrator account in Windows). The remaining accounts will be allocated for the users and for certain applications.
Yes.
By default,there is only one account, root. However, most Linux distribution will either allow or make you set up a second administrative user account.
Yes, as long as they have user accounts on both machines.
You can't recover passwords in Linux; you can only reset the passwords on various accounts.
The operating system included with this Netbook is HP Mobile Internet, which is built on Linux. So, yes, this Netbook is compatible with Linux.
You do not need to install PuTTY in Linux as there are built-in utilities that can do PuTTY's job (ssh, telnet)
There are an abundant amount of securities in Linux, and most Linux distributions. It would take an extremely long time to list out every "Security" in Linux, as it's built around securities.
Built in user accounts
there is no "linux operating system". linux is merely a kernel that operating systems can be built upon, of which there are dozens if not hundreds
Linux is an operating system on which a wide array of system distributions (Such as Ubuntu and Android.) are built.
Linux is an operating system on which lots of system distributions, such as Ubuntu, Android, Chrome OS, Archlinux, are built.
With most Unix-derived systems, "root" is the super-user account.