How can I access the photos in my iCloud and how can I delete them?
See -> Manage your iCloud storage
Manage your iCloud storage - Apple Support
I've been getting notifications on my phone saying I have no space
Do you mean iPhone device storage?
Then try to free up iPhone device storage see this Apple articles below:
If you need more space for an update on your iPhone, iPad, or iPod touch
If you need more space for an update on your iPhone, iPad, or iPod touch - Apple Support
How to check the storage on your iPhone, iPad and iPod touch
How to check the storage on your iPhone, iPad and iPod touch – Apple Support (UK)
Clear Other storage on your iPhone or iPad
Clear Other storage on your iPhone or iPad - Apple Support