iCloud and photos

I am so confused about iCloud and photos.

I download my photos from phone to my computer into Photos. Then I want to delete them from my phone. I want them gone from the phone, not coming back all the time. I also am now getting pop up photos on my ipad, which I don't want.

I recently bought cloud space because I thought I couldn't export a 10 min video. I'm not sure the space had anything to do with it. I also lost some pictures when I messed with setting on my phone.

But this is far too confusing for me and I'm afraid to plug phone into computer for fear of having more photos put BACK on my phone and then messing up my system in computer Photos.

Does this make sense? Thanks. Kris