icloud extra storage - photos

You can’t buy extra storage for your iPhone; it will never have more storage than it had when you bought it. What you bought is iCloud storage on Apple’s servers; this space is for backups and content syncing. But the key word is “syncing” - anything in iCloud is duplicated on your phone, and if you delete something from your phone it will also be deleted from iCloud.

To sync photos to iCloud, on the phone go to Settings/[your name]/iCloud and turn on the switch for Photos. Then leave your phone plugged in and connected to Wi-Fi so the photos can sync to iCloud.

Yes, your plan would work as long as your Internet connection is good and your phone is logged in to the same Apple ID that you go to https://icloud.com and log in with. Once they are in iCloud you can download them from iCloud to your computer, or just view them in the Photos app on your Mac and export them from Photos to your external drive.

But it should also work to use a USB connection to your Mac as described in this Apple support article—>Transfer photos and videos from your iPhone, iPad, or iPod touch - Apple Support, and that would be much faster.

That depends on your Internet connection speed. Did you turn on photo sync as I described? Are you connected to Wi-Fi on the phone? Do you leave the phone plugged in? Assuming an average photo size of 4 MB, 10,000 photos will occupy about 40 GB (you can verify this by going to Settings/general/iPhone storage and see how much space is occupied by Photos. If you have, say, a 100 mbps network connection, which corresponds roughly to 10 megabytes per second, it will take about 4,000 seconds or about 1 1/2 hours. If your network connection speed is only 10 mbps it will take about 15 hours.

But remember that uploading your photos to iCloud will not free any space on your phone. Your photos will still be on your phone, and will take up that same 40 GB. And you can’t delete them from your phone, because that will also delete them from iCloud.

If you want to free space on your phone you should sync your photos to an archiving service such as Google Photos or Dropbox.