Hmm,
Right few issues here the Laptop HDD seems to be NTFS, I would guess that the External one is FAT32 (or it should be) or course if you were to format the external to NTFS you would lose your data.
You are going to have to get the files off the external before you can add an OS to it (or you could lose some of your data)
You normally have a system recovery disk/ or a recovery partition, not both.
You are going to have to move the info from the external to the other HDD then format the external and install the OS to it, then transfer the data back from the (old) lappy HDD to the (new that was external)
Make sense?