You'd have to use the Stack Exchange user ID: http://stackexchange.com/users/login.
This is the account_id, to be more precise.
With that, run the User's associated accounts method.
Iterate through the results running another query (with your user_id in each site) to build the favorites:
"site_name": "Stack Overflow",
There are separate RSS feeds for Hot/Week/Month, etc. EG:
The API /questions route offers equivalent sorting options for Hot/Week/Month. EG:
This is most likely one of those things you'll have to do yourself and one reason why the API is available.
And, it's not too hard; here is pseudo code that works:
Call /questions/featured with max page-size and (ideally) filtered by your tag(s) of interest. EG:
Page through the results until has_more ...