1) CRUD access is not provided to any two of them such that a user has access to only one object at a time. Then what would be the sharing and visibility of related object's records.
Since, OWD is private then only the Owner will see the record. If CRUD access is not provided then use will not see those records and not even access those by clicking recordIds.
2) CRUD access is provided - What would be the visibility for the related records.
If the CRUD access is provided then for all the related records must be shared to the user by Sharing rules or other different ways. User has access to one record doesn't mean he/she could have access to all related records available via Lookup relationship.
Also, is the implicit sharing different for Standard objects and Custom objects ?
Yes, implicit sharing is different for Standard and Custom Object. For example, in a private sharing model, if user has read access to Account record then he will have read access to all the related records of Account, like Contacts, Opportunities, Cases.
Similarly, If user has access to Case record then automatically he will have access to parent Account record.
This doesn't apply to Custom objects.