Q: If I delete BACKUP from my iCloud to make more space

Backup keeps your data stored so if you ever get a new iPhone or you reset or wipe your current iPhone, you can restore from your backup and you will get all your data back on your phone. Think of it as a 2 chance to get your stuff back if something happened to it.

If you delete your backup you will no longer have a backup to restore, new backups will not be affected.

To directly answer your questions:

If you have enabled automatic backups, then it will start backing up the data from that point forward.

If you get a new phone, the backup on your old iPhone will be there until you delete it.  (If you have enough space you can have a backup of your old phone AND new phone at the same time.)

In general, these may help:

iCloud: Back up your iOS device to iCloud

How to back up your iPhone, iPad, and iPod touch - Apple Support

Personally, I like to maintain an iTunes backup as well.  I consider the iCloud backup as a backup for my iTunes backup.. But that's just me.

An iTunes backup contains the same information as an iCloud backup.  But with iTunes, you can separately store your purchases (Apps & Music) and sync those to your iPhone if you need to.  This article explains the difference between an iCloud & iTunes backup:

About backups in iCloud and iTunes - Apple Support

In either case, the space on your iPhone remains the same.  If you really need to save space on your iPhone, you can copy the photos to your computer and then delete them from your iPhone.  See this article:

Import photos and videos from your iPhone, iPad, or iPod touch - Apple Support