Is it possible to delete photos from phone or device and not from iCloud?

iCloud Photos is a syncing service. Any photo you delete from a device where iCloud Photos is turned on will also be deleted from iCloud and from any other device connected to iCloud Photos. You can potentially reduce the storage space required on a device by turning on Optimize Storage. See: https://support.apple.com/en-us/HT204264

Apple does not currently offer cloud-only storage for photos. If that is what you want or need, you may want to explore 3rd party options such as Google Photos or Dropbox.

Another way that photos may be on iCloud (if you don’t have iCloud Photos turned on) is via a backup of an iOS device. The only thing you can do with a backup is use it to restore a device or set up a new device. The contents of backups are not viewable at iCloud.com and if you delete a photo from a device it will not be included in future backups and will be lost.

My “other” category in the iPhone storage is the majority and I deleted all my cache’s etc, all the things I was told to do after a google search. I want to reset my phone.

You may want to consider updating to iOS 13.6.1

https://support.apple.com/en-ca/HT210393

Before you restore your phone, try updating to iOS 13.6.1. This is supposed to fix the problem with “other” storage.

Clear Other storage on your iPhone or iPad - Apple Support

When you backup your device, your backup won’t be any where near the size of all of the content on your phone. For instance, Apps are not included in the backup. When you restore a backup, you also restore your purchase history and all of your apps will download from the cloud.

You can read this to get a better idea of what backups include.

About backups for iPhone, iPad, and iPod touch - Apple Support

If you use iCloud Photos, that simply keeps your photos in sync across your devices. Your photos are not stored in iCloud like you would store photos on a hard drive or on your computer. If you delete photos on your device, they are deleted everywhere. There is a recently deleted folder in the photos app where deleted photos reside for 30 days and after that they are gone.

If deleted photos come back, something funky is going on with iCloud. They should not come back after they have been deleted for 30 days.

Regarding the "other" category, that is a separate issue. There was a storage problem that was fixed by iOS13.6.1 that was released a day or two ago so if you haven't installed that you may want to see if that helps with that issue.

If you have iCloud Photos turned on in both your iPhone and your computer, the photos are automatically synced between the two. The sync dynamically (after any change) between iCloud and each other.

I don’t know if this will be of any help, and if you don’t have a computer, that eliminates one suggestion, but take a look.

If you need more space for an update - Apple Support

You may want to make a new post with that in the title -- I don't have any particular expertise with that but a post with that in the title may attract someone who does.