how to disable all connection of all link of prestashop?
As long as you don't use the BO to update purchased modules you should be able to remove the native PrestaShop's module below.
Start by inactivate (disable) the modules.
Personally I conciser it a security risk to keep a disabled module on my server, even if it is disabled. So when I know when I don't need it anymore, I uninstall it and delete it.
Remember to do backup before deleting anything.
The following modules should be safe to inactivate/disable and eventually uninstall.
By disabling then it should at least reduce the API calls to prestashop.
Module: Tips and Updates module
Technical name: psaddonsconnect
What it does:
Connects to Addons marketplace. Disable if managing modules manually.
Module: Merchant Expertise
Technical name: gamification
What it does:
Adds gamification badges in back office. Purely cosmetic.
Module: Welcome
Technical name: welcome
What it does:
Displays welcome onboarding widget in back office.
Module: PrestaShop Marketplace in your Back Office
Technical name: ps_mbo
What it does:
Provides the “Module Catalog” interface in your BO, allowing you to:
-Browse PrestaShop Addons modules.
-Install or buy modules directly from the marketplace.
-View recommendations and promoted modules.