Migrate from MacBook Pro to external hard drive

I have a MacBook Pro with no video, external monitor won't work, it's the nvdia chip. Before working on it, I want to back up the Apps, Settings etc. I have the data backed up. I tried to migrate to my mac mini but it doesn't have enough space so I thought I could migrate to my external hard drive, but I can't see the external... Here are my 3 inital questions:

Can you Migrate from Macbook to external drive....if so, how...migration asst. or disk utility????

When you Migrate from one drive to another, does it overwrite the files on the new drive, in this case my Mac Mini

Can you clone or disk image to an external hard drive, if so, how?