A) Yes, if you select the category then the post from that category will be displayed. I just check your site and it’s showing just 3 of them on the homepage.
B) Yes, that also controls the Post Page. So, if you want seperate then please use as “Featured Content”. Go to “Appearance => Customize => Featured Content”, select “Homepage / Frontpate” on “Enable On” options, select “Cateogry” on “Type” option and then select “Categories” as per your need in “Select Categories”. In this way you will have seperate posts for homepage and all other in post page.

Regards,
Sakin