Q: Is the emulator as responsive as a normal android phone (of course this depends on the exact phone but in general)?
A: Absolutely not! The worst example is the 3D, which is, afaik, only software emulation.
Q: Is there a way to control the memory on the emulator?
A: Please specify, the size of the SD-Card is configurable, the RAM/VM-Memory... I don't know.
Q: Has anyone had issues that have been flagged on the phone but not the emulator? or vice versa?
A: Each device has his own customization. On the emulator you can only change the screen resolution, but caution: the size of your Emulator screen depends on the pixel density you set up. So what might look good on your big emulator could be too tiny on a real device. And don't forget, a finger is much bigger and not as accurate as a mouse cursor.
Q: What's your normal testing procedure to test on both throughout, or emulator recursively and phone at the end?
A: Functionality is tested during the implementation mainly on a (fast) device, like a Nexus One. The real test after implementation will be on as many devices as possible. The UI, too (most differences there)
Since I have a device which is has the latest SDK, I prefer testing on the device. Thats not necessary for programming an app, but please: don't publish an app without at least one test round on a real device :)