Every endpoint is independently rate-limited. So you could do your thing with favourites, and also independently grab a timeline - the two limits are separate.
User auth and app auth are also independent. You can have many users all logged-in to your account able to call endpoints on their own limits, and then there’s also app auth (which may not allow access to some functions, such as posting Tweets, but can work with others).
If you want access to more streaming data than the 1% provided on the public streams, you should look at our commercial Gnip data offerings. The statuses/firehose endpoint is documented for legacy reasons and is not available for new applications. You can use our platform support forms for special requests, but these are rarely granted.
