Example, today I bought PowerAge's Architecture bundle which includes "Mon Quartier". In "My Account"/ "Purchased Items", the bundle shows up but not the "Mon Quartier" individual item. Also, on the product page for "Mon Quartier", it does not show that I have purchased the item. All the individual items purchased in bundles should show up in the "Purchased Items" list, and the item product page should show it as "Purchased".

Yes, that is currently how bundles work. We have this on our to-do list for improvements...but right now this is correct behavior.