You have a MacAir so, if you're using iCloud, then all the pictures are in MacAir Photos. If you're not using "Optimize Storage," then Time Machine backs up the pictures, already. And another excellent backup step is to drag the Photos Library from the Pictures Library to a separate external drive, maybe once a month.
If you are using "Optimize," then things are rather harder. You can go to iCloud.com>Photos and download pictures fro there. You would need to go into Safari's Settings>General and set the download target as your external drive. Then select pictures (it must be less than 1000) and choose download, then the next 1000, and so on. But here's the problem-- do you want the pictures as you've edited and commented and cropped them, or do you want to archive the Original Files that haven't been altered? If you want both, then you'll have to do everything twice, and take up twice the storage space.
The first method, saving the Photos Library, is by far the better option. The Photos Library has the Originals and all the information that turns the Originals into the edited versions in not much more space than the Originals take by themselves. Also, the Photos Library has even more information about faces, objects, and so on. But this is only possible if you've chosen "Download Originals" instead of "Optimize." The "Download Originals" option also allows Time Machine to back up your pictures on a regular schedule.
I use "Optimize" on my phone, but I don't choose it for my Mac, because I want to backup my pictures.
If you've had "Optimize" turned on, and then you change to "Download Originals," then the downloading does not take effect immediately-- you would need to force downloads.
As Niel says, none of this removes pictures from Photos at iCloud.com or from Photos on your Mac.