After subscription if we delete some pictures or videos from our phone, will these photos and videos be deleted from iCloud storage in next daily / weekly or monthly update?

After you enable iCloud Photos on your iPhone, the iPhone will sync with iCloud Photos and the photos in iCloud will always be identical to the photos on your iPhone. Any photos you delete from the iPhone will instantly be deleted from the iPhone and iCloud Photos and any other device syncing with iCloud Photos as well. So you must not delete any photo on your iPhone, that you want to keep in iCloud.

The only way to save storage on your iPhone with iCloud Photos is to enable "Optimize iPhone Storage" in the settings for AppleID > iCloud > Photos. The iCloud will automatically remove the high resolution originals of the photos and videos you have not used in a long time from your iPhone and replace them by smaller previews for viewing. Your most recent photos will be kept at the full resolution, as space permits. This is fully automatic.

See: Use iCloud Photos on iPhone – Apple Support (UK)