So right now your pictures are being stored in iCloud and that is how on your Macbook Air you are able to see them in the Photos app if your signed in with the same iCloud account on your MacBook Air as your iPhone, if you turn off iCloud then your phone will not get backed up nor pictures messages and contacts and anything other things in iCloud. If you wanted to turn off iCloud photos you could do so by going into Settings > Click your name at the top and then > iCloud and turn off the green button next to photos.
Then the only downside is if you lose your iPhone with all the pictures on it then they will be gone forever, since there not being saved in iCloud.
As far as taking all the pictures on your iPhone and moving them over to your mac, follow this article.
Transfer photos and videos from your iPhone, iPad, or iPod touch - Apple Support