I believe such views are usually referred to as theistic evolution whereby an intelligent designer is responsible for some aspect of the evolutionary process.
Just one quibble. ID is not TE. The idea that GOD created all that is seen and unseen does does preclude GOD using totally natural processes.
If you would like the answers to some of your questions from a TE perspective, the
Catechism of Creation is a good place to start.
Aslan is not a
Tame Lion