I think you have the numbers right, but to make certain just select a type 7, level 5 MIC with no (or 'all') unit types selected for your faction. Then look at the 'Select Unit' drop down menu and if you see the elite units that are specific to your faction listed, then the MIC type represents your native government.

I believe you can build a regional MIC irrespective of the government type, however the type of units that'll be available to you will be more restricted under a factional government.

I also think that if your empire expands quickly, you'll most likely have to rely on client rulers working under type IV govs. In my so far limited experience with them, I haven't been very lucky with their starting traits, but I can't see any other way to provide governance to important expansion cities without them cuz of the limited amount of FMs you're provided with when you're taking significant amount of territory with speed. If you have a more measured approach to conquest, then of course it's highly probable that you'll have more FMs to work with as the years progress. However I think that eventually you'll have to make considerations for them regardless, when your empire expands and becomes massive beyond your capability to govern within your own family.

Of course you can always change government types at a later date as well.