1) You don't really block a user from configuring a corporate resource in the personal profile, but you block their ability to connect to that resource using Conditional Access. Conditional Access is an AAD feature that blocks access to AAD authenticated resources based on the state and compliance of a device including traits like the profile and application being used. Intune defines extended information that feeds into CA.
2) Kind of. The actual technical details are app specific and thus it's ultimately up to each app to define this.
3) Yes, using app config policies, see https://www.inthecloud247.com/manage-edge-mobile-favorites-with-microsoft-intune/. Also see for complete Edge management details https://learn.microsoft.com/en-us/mem/intune/apps/manage-microsoft-edge