Suggest any azure service which
Service to connect/query Azure AD : Microsoft Graph API can help you query Azure AD
Sync changes between two different Azure AD tenants: AFAIK there isn't any service that will do this for you, you need to write something custom yourself that can make use of Microsoft Graph API
Notification on changes: Microsoft Graph API supports change notifications for some scenarios.. User and Group resource types are supported.. see if this covers what you're looking for Use the Microsoft Graph API to get change notifications
Incremental changes: Microsoft Graph API also supports delta queries for some operations, which could help in figuring out incremental changes.
Authentication: Most probably client credentials grant flow using Application permissions, with a daemon app would make sense for such scenario. Although, this is something you'll need to decide based on how you finally implement.
Permissions required: Microsoft Graph API permissions reference
Function or WebJob or something else: it's a little subjective I guess. I don't have a clear single recommendation. WebJob might be better if it turns out to be long running, but I'm not sure. You may need a separate question or find some already answered good questions about this.