So, what's the difference between the capital letter nationalities and the lowercase?

The same as the difference between Chinese and chinese. Mchina (capitalised) is correct to my knowledge.

When do I add the double m?

You don't "add" a double m to anything. It just happens naturally in the word Mmarekani because Marekani (one m) refers to the US and m- is added to the beginning. So China + m = Mchina; Tanzania + m = Mtanzania; and Marekani + m = Mmarekani. Like how in the word "unnamed" there are two n's.

[2019/04/02]