If I buy iCloud storage can I update my phone and other apps as well?
Yes, you do get more space for your iPhone in some sense. Your iPhone uses iCloud for backups (probably; you can choose not to do so), and storing photos and other documents which don't need to be on your iPhone, leaving more 'disk' space there. Note that App Store apps themselves don't take up space on iCloud - they're backed up 'for free', but their settings and document might take up space.

If you downgrade / cancel your subscription, the official Apple support page only mentions you cannot 'upload' anymore to iCloud. While that doesn't mean the photos will stay there forever, it does imply you get the chance to remove certain content in order to get below your new limit, so it is at least kept for a while.