Hi and welcome to Arturia forums.
Can you download your purchased soundbanks from your account thru the website (not thru Analog Lab)?
When downloaded then run the soundbank installer on your computer.
About issues with the store, i suggest you contact Arturia support directly thru your account.
I don't know if you are supposed to see the presets in the store - at least before you put them in the bag, and perhaps even before they are installed on your computer.
Keep in mind that when you have purchased, downloaded and installed a soundbank, then you don't have to be in store mode to select the presets.