Ut stores the avatars on the server, cached by all parameters (not the name, but the generated initials) to avoid generating them again. Also some response headers are set to ask browsers to cache the response. I would also recommend users of this to download the avatars, as you suggested, especially to ensure fastest possible response rates.
Actually there is no rate limiting, but seeing just how many visitors this HN post has gotten, I may have to add some sort of limiting.
I haven't really figured exactly what I'm going to do regarding limiting and servers. Currently I'm setting up servers in each region my provider supports, to fix latency issues, and spread the load