Will canceling my icloud+ storage subscription delete everything? + Why wont my phone wont back up even though I have enough space?

Hello,

So I bought 50GB of iCloud+ storage because I was worried I would damage my phone and lose everything.

After I purchased it I received a receipt in my email stating that it was billed to my dad's card (I previously used his card to buy something on a game), I want to cancel the subscription, remove his card, add my card, and then repurchase the subscription. I am just worried because I have years of photos on my phone and don't want to lose them. I tried to go back up but it says I don't have enough space. Please see the images below, I need the help.