>When I started the Apricorn Clone Software (with hardware) connection, it automatically includes ALL current drives on my PC as the source. And the F: RECOVERY is included. And I see no way to exclude it :(.
>Question: Once the PC is cloned to the new drive, will I be able to "kill" this F: RECOVERY drive? Because according to the suggestions, I have no need for it. Please let me know.

You should be able to delete the partition later and re-create it as a new partition, or to extend a nearby partition to use the available space. Disk management software should be capable of that.