More detailed quick start guides and things should be coming, but here are the answers to your questions:
1 - If you assign a monitored product to a distribution package - what's next? Does it get installed? Why and When?
The package will get installed during the Install Mapped Software action in a Provisioning template IF the product was found on the device previously. In the case where you are doing a machine to machine migration scenario and this is the destination machine that you've setup in your machine to machine mapping tool then it would install IF the product was found on the source device previously.
2 - Does machine mapping replace profile migration? How does it work?
Machine mapping does not directly replace profile migration, but it does work alongside it. From a technical standpoint a machine mapping will let certain actions intelligently use information from a different machine than itself. Note that any computer that does not have a mapping will just treat itself as the source and the destination, all the actions will work for in place upgrades as well as machine to machine upgrades. I'll list those actions here:
Deploy Profile (when using the auto naming option) - When doing a Deploy Profile action provisioning will look to see if this is a destination machine in the machine mapping tool. If so, we know that we need to get the profile that was made from the source machine, so the auto-naming option will try and find the old machine's profile to bring it forward.
Launch Template - This is a special action that was custom built to take advantage of the machine mapping. The idea here is that I can have my old machine start a template that has something like profile capture or any other pre-flight tasks and then when those actions succeed it will launch a deploy template on the destination machine, so you get your end to end migration by just starting one task. As I mentioned before, the profile deploy action on the destination device would then successfully apply the profile that you captured from the source.
Install Mapped Software - This action is what was described above. The idea is to install the software you had previously based on intelligent rules configured by the admin. If I'm moving from device to device, however, I don't want to know what my new device has (probably nothing, because it's new), I want to know what the old device had. When this action is run on a destination machine it will install the software, but based on what was on the source machine.
I believe that's a quick summary of what those tools do and what they're for. Let me know what additional clarification you need.
Thanks, Mach. Sorry for the delay in responding, but this is good info.