I\'m looking to create a (REST) API for my application. The initial/primary purpose will be for consumption by mobile apps (iPhone, Android, Symbian, etc
That's a whole lot of questions in one, I guess quite a few people didn't manage to read all the way to the end :)
My experience of web service authentication is that people usually overengineer it, and the problems are only the same as you would encounter on a web page. Possible very simple options would include https for the login step, return a token, require it to be included with future requests. You could also use http basic authentication, and just pass stuff in the header. For added security, rotate/expire the tokens frequently, check the requests are coming from the same IP block (this could get messy though as mobile users move between cells), combine with API key or similar. Alternatively, do the "request key" step of oauth (someone suggested this in a previous answer already and it's a good idea) before authenticating the user, and use that as a required key to generate the access token.
An alternative which I haven't used yet but I've heard a lot about as a device-friendly alternative to oAuth is xAuth. Have a look at it and if you use it then I'd be really interested to hear what your impressions are.
For hashing, sha1 is a bit better but don't get hung up about it - whatever the devices can easily (and quickly in a performance sense) implement is probably fine.
Hope that helps, good luck :)