Create MSI file with product key

The type of tool you're looking for is called an Application Repackaging tool. The process would include capturing an installation (take a machine snapshot, run your installation and make customisations, then run a second snapshot to calculate the differences) then compiling the captured data into MSI format.

The following are some free tools to perform these tasks, in order:

1. AppDeploy Repackager: Use this to capture your installation and create an MSI from the captured data. If your app is reasonably simple then this may be all you need.
2. Microsoft Orca: Use this to edit the MSI that has been created with AppDeploy Repackager. You will need to know how MSI's work to really make the most of Orca. Microsoft's Installer Database Reference is the definitive source for information on MSI contents.

As for your second question: You will find that sometimes vendors will supply an MSI wrapped in an executable, so if you run the .exe you might be able to dig out the MSI from a temp directory.

After working with Microsoft on this issue the only decent solution was the following:

Pranav, from our Install team, informed me that he was able to figure out the issue. He explained to me that you wouldn’t be able to install with an msp, remove office, and then reinstall with the same msp when modifying the ‘.NET programmability support’ feature under ‘InfoPath’.
Apparently the issue can be resolved by creating a new msp with the same settings as your original msp.

This appears to be the only workaround for the issue of other Office updates causing the .msp file to fail as well.

So, we decided to do the following:

1. Create the .msp patch and deploy it via a computer startup script
2. "Re-save" the .msp patch once a day for 2 weeks while deploying to make sure it takes affect on the client computers
3. In the script the client computers will "report back" to a central log file (append it) with their computer name and a yes/no response.
4. After 2 weeks we'll use the "no" responses we get back to go manually hit those machines and fix them.

It's sucky, but it'll have to do. We'll update our base computer image for the future so we don't have to deal with this again.