What is the btc.to address shortening algorithm? How does the btc.to address shortening algorithm work? Is is a deterministic algorithm, that is, it can be reproduced on other websites with the same results, or are the results specific to the website and the order in which the addresses were inputted?
The results are specific to the website and the order in which the addresses were input.

This can be easily determined by experiment. I took a random address from BE and it gave me http://btc.to/2z7. I took another address and it gave me http://btc.to/2z8.

So clearly, it stores all given addresses in a database, and the URL is the address ID encoded in base 36 (experiment also shows that it's case insensitive).

Also, it only accepts valid Bitcoin addresses.

More generally, it's impossible for any algorithm to take an arbitrary long, high-entropy string and give a short string which can be uniquely mapped back to the input.