Just so you know, doing an iCloud backup is not going to free up any space on your device. It is only going to back up what is on your device in case you need it to restore your device. If you need to free up space on your device, go to Settings>General>Usage, and under the first Storage section, see what is taking up so much room on your phone.
Delete any unneeded apps, delete mail, text messages with videos and photos, remove photos from your Camera Roll if you have imported them to your computer, etc.
If you set up a separate iCloud account, then everything associated with the other iCloud account will no longer be there. Contacts can be preserved by "Keeping them on your Phone" when you delete the original iCloud account (it will ask you if you want to do that). Then, when you add the new iCloud account, you can "Merge" them with that account so you still have them.
Apps are associated with your iTunes account, and you can have a separate iCloud account from your iTunes account (see the section "Using one Apple ID for iCloud and a different Apple ID for Store Purchases":
Using your Apple ID for Apple services
To create a new iCloud account, you are essentially setting up a new Apple ID. Here is another helpful support article about setting up a new iCloud account:
Creating an iCloud account: Frequently Asked Questions
Cheers,
GB
