1. First, would there be any way to make this (or a different model YubiKey) to provide one factor authentication? By this, I mean that when a user is prompted for a password in Windows OS, an application. a webpage, etc; they could insert their YubiKey and it would grant access. Sinilar to how it works out of the box - but no need to type a physical password.
YubiKey is a One-Time-Password generator device that also supports other interesting modes/features like:
a. Static Password Mode
b. HOTP mode
c. Challenge-Response mode
Yubico also provides supporting software modules for customers to implement YubiKey integration as per their own needs; so in theory it is possible to implement only YubiKey OTP based one-factor authentication.
It really depends on the application vendors/service providers what approach they take and options offered to the end users depending on the threat model and security requirements for their application/service.
2. What (if any) applications would anyone recommend to use with the YubiKey? I'm not asking which ones are compatible for authentication, but ones that would allow me to do neat things or program it.
Please visit http://www.yubico.com/developers-intro
as a startting point for information and further links to the software modules and documentation offered by Yubico.
Yubico offers personalization tool to program YubiKeys; please visit http://www.yubico.com/personalization-tool