It is not possible, at least not within reason, to solve either of these issues due to fundamental limitations of PHP in a web envionment (mod_php).
Class variables do not persist between web requests, so the Keep-Alive part of the problem cannot be fixed because all the resources (i.e. curl handle, tcp socket) will be destroyed at the end of the request. Re-using the cUrl handle seem to be mostly relevant to batch scripts or the rare web-script that needs to access multiple URLs in one go. The kind of performance optimizations considered standard for Java developers are therefore unavailable to PHP developers.
One could try to implement digest authentication by sticking the values for the Authorization header into session, but that is not cheap to implement (high dev time) and not something that many enterprises want to dedicate time to. This might be a nice 3rd year university project for example.
Hopefully, at some point, someone will release an add-on product for PHP in Apache that somehow channels HTTP requests through to a TCP connection pool external to the process. That would probably make money, given that it will knock a lot of latency off upstream HTTP requests from PHP.