[Is Littlefinger based on Caligula?]

Definitely not. Gaius Caligula was nuts, and Petyr Baelish is as sane as can be. Caligula was flamoyant and drew attention to himself. Littlefinger is more subtle.

[Why is Tyrion so great, and what inspired his creation?]

He's drawn from a wide variety of sources. Including myself. I'm taller.