Can I store data in iCloud and how do I do it?

You can’t store data in iCloud and then remove it from your phone to free up space on the device. That is not how iCloud works. iCloud keeps data in sync across your devices and it does allow you to save a little bit of storage with regard to photos, if you use iCloud Photos, but it is not archival or off device storage. If you delete data in iCloud you delete it everywhere, unless you archive the data and store it on a computer. If you do that, then you can delete it from the phone.

You need to either buy a phone with more local storage or delete some content from the phone.

You need to delete content on the phone in order to have more available space. You cannot add physical storage to the phone so your only alternative is to remove content to free up space.

Take a look at this.

How to check the storage on your iPhone, iPad, and iPod touch - Apple Support

This one may be helpful as well.

Manage your photo and video storage - Apple Support

If you have a receipt you have paid for it and will do so every month. As he explained this will not put more storage on your iPhone.