Just on the first question of countries of origin for muslim immigrants to the US:
The biggest group is people from South Asia, so Pakistan, Bangladesh, India (due to the nature of the partition of India, the majority of South Asian muslims were either already living in the territories that would become Pakistan/Bangladesh, or were forced by violence to cross the new border into Pakistan/Bangladesh; TL;DR the former two are much more likely countries of origin).
The next largest grouping of Muslim US Americans is people from the Middle East and North Africa. In my quick research I haven't been able to find a good further breakdown by country, but the strategy I would use is to think historically. When did your character or your character's family come to the US, and what was going on then in different countries of the region that might prompt somebody to leave for the US?
Other parts of the world with significant Muslim populations are Central Asia, Malaysia and Indonesia (the latter is the most populous majority Muslim country in the world), West African countries such as Senegal or Niger, and coastal East Africa like Tanzania and Somalia. People from these countries aren't as likely to end up in the US whether from poverty (moving a long way is expensive), or because of differing colonial histories (most countries in West Africa with significant Muslim populations were colonized by France, so people there are more likely to speak French already and choose to emigrate to France over other European/Western countries). Of course, that doesn't rule out any of these countries. As little examples, my small university city secondary hometown has an Afghan restaurant run by a family that came here from Afghanistan, my Calc II professor's husband was Malay, there are plenty of Somali Americans.
It'll be a lot easier to answer your other questions once you have an idea of where your character is from!
ETA: you can also approach this from the other direction. Where in the US do they live, and what immigrant communities are found there? Look up different neighborhoods in whatever city you can think of, see what stores and restaurants and places of worship you find on maps.
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The biggest group is people from South Asia, so Pakistan, Bangladesh, India (due to the nature of the partition of India, the majority of South Asian muslims were either already living in the territories that would become Pakistan/Bangladesh, or were forced by violence to cross the new border into Pakistan/Bangladesh; TL;DR the former two are much more likely countries of origin).
The next largest grouping of Muslim US Americans is people from the Middle East and North Africa. In my quick research I haven't been able to find a good further breakdown by country, but the strategy I would use is to think historically. When did your character or your character's family come to the US, and what was going on then in different countries of the region that might prompt somebody to leave for the US?
Other parts of the world with significant Muslim populations are Central Asia, Malaysia and Indonesia (the latter is the most populous majority Muslim country in the world), West African countries such as Senegal or Niger, and coastal East Africa like Tanzania and Somalia. People from these countries aren't as likely to end up in the US whether from poverty (moving a long way is expensive), or because of differing colonial histories (most countries in West Africa with significant Muslim populations were colonized by France, so people there are more likely to speak French already and choose to emigrate to France over other European/Western countries). Of course, that doesn't rule out any of these countries. As little examples, my small university city secondary hometown has an Afghan restaurant run by a family that came here from Afghanistan, my Calc II professor's husband was Malay, there are plenty of Somali Americans.
It'll be a lot easier to answer your other questions once you have an idea of where your character is from!
ETA: you can also approach this from the other direction. Where in the US do they live, and what immigrant communities are found there? Look up different neighborhoods in whatever city you can think of, see what stores and restaurants and places of worship you find on maps.