I want to logon to iCloud to view and manage my data on my iPhone so I don’t have to upgrade my storage?

Any photos stored in iCloud would appear in the Photos App on your iPhone.

You can if you choose to access the http://icloud.com website from a computer and access the Photos App there to view any photos stored in iCloud.

Alternatively, you can, on your iPhone, go to Settings->Account(top of Settings)->iCloud->Manage Storage, to get an overview of what is stored in iCloud, and options to delete it.

No, you do not "have" to buy more iCloud storage.

See here for more details: Manage your iCloud storage - Apple Support

to use iCloud you must purchase adequate storage - give this a read - Manage your iCloud storage - Apple Support

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If you are syncing photos to iCloud, if you delete them from iCloud, they will delete from your device.