I'm one of the developers on Cloud Functions for Firebase and would be happy to answer any questions you have. I'll try to keep my responses to my product alone since I think other team members are more qualified to answer those.
Your feedback is both fair and something we're diligently working to fix. In response to each of these points:
1. [Local testing only works for HTTPS]. For better or worse, our product is built in layers. There's the core Cloud Functions product and the "for Firebase" add-ons. You can already see some public changes we've made to the core Cloud Functions emulator that include some support for event-handling Cloud Functions as well as improvers in debugger support. We definitely want better "in house" support and are in the user testing stages of some generational leaps in local testability with the Firebase toolchain. You can reach me at my handle at google.com if you'd like to be considered for some of the user testing.
2. [Debugging feels like a murder mystery]. Yes, this is another thing we are working on. Cloud Functions integrates with Stackdriver Debugging[1]. There are very real issues with the integration today. TL;DR: If you have a steady stream of requests, it will work. If not, the ephemeral instances won't be alive/unthrottled long enough to fetch watchpoints. This is a huge concern to many of us within Google and we're working hard to improve the way it works.
3. [No cron jobs]. Again, a huge feature request and a high priority. You don't need to use your own machine; you can use GAE's free tier to kick off cron jobs for you[2]. Still, a more tightly integrated solution is obviously ideal and is coming.
Closing: We take these issues very seriously. I'm sorry we don't have the solution to your problems today, though all three line up with active development on the team. We are focused on delivering infrastructure required for mature apps with high volume and mission critical traffic. Keep an eye out for our product as it crosses into generally available and beyond.
[1]: https://cloud.google.com/debugger
[2]: https://github.com/firebase/functions-cron