Can I use my iPhone while I am backing it up?

If you are doing an automatic backup, the screen has to be locked.

To let iCloud automatically back up your device each day, here's what you need to do:

• Make sure that iCloud Backup is turned on in Settings > [your name] > iCloud > iCloud Backup. If you’re using iOS 10.2 or earlier, go to Settings > iCloud > Backup.
• Connect your device to a power source.
• Connect your device to a Wi-Fi network.
• Make sure that your device's screen is locked.
• Check that you have enough available space in iCloud for the backup. When you sign in to iCloud, you get 5GB of iCloud storage for free. If you need more iCloud storage, you can buy more from your iPhone, iPad, iPod touch, or Mac. Plans start at 50GB for $0.99 (USD) a month. Learn more about prices in your region.

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

Yes, you can manually start a backup from Settings->Accounts(top of settings)->iCloud->Backup->Backup Now.

Then exit the screen and do whatever you want.

Yes.