backing up pictures

I cannot get my head around how to deal with pictures taken with my iphone 5, 16 GB. I am on iOS 9.2.1 and OS X 10.10.5. I want to be able to take a picture, have it transferred to my computer and then wipe it on my phone, since eventually I will run out of space.

If I take a picture with my phone it appears in my Camera Roll and then My Photo Stream on my phone. I can also after a while see it in iCloud on the web and it is also visible in Photos on my Mac.

1. If I delete it from my My Photo Stream on my phone, it can still be seen in my Camera Roll, on my Mac and in iCloud.

2. If I delete it from my Camera Roll on my phone, it disappears from My Photo Stream on my phone but it can still be seen on my Mac and in iCloud.

So, is this correct or am I experiencing a delayed reaction in iCloud and on the Mac? Does this mean that I can delete all my pictures from my Camera Roll after all the pictures have been uploaded via wifi to iCloud or by cable to the Mac?