In what ways can I separately manage entries in Contacts.app and SIM card contacts?
My answers are only about usual not jailbreaked iPhone


You can import contact from SIM, more on this here. It's not possible to export contacts to the card.
It is not possible to view the contacts that are stored on sim/iPhone separately.
The default memory storage for contacts is iPhone memory. Can't be changed.
Here is a universal way to delete all contacts from Address Book. iPhone can't delete contacts from SIM card.