Q: I want to change my email address in iCloud

Is your device signed into iCloud using an old ID now?  If so, does the old ID belong to you?

If it's an iCloud backup, you restore it as explained here: iCloud: Restore your iOS device from iCloud.  If your backup is on your computer, you restore it using iTunes by connecting your new phone to your computer, opening iTunes, then going to File>Devices>Restore from Backup.  (If you are using a PC and don't see the File menu at the top, you may need to reveal it as explained here: iTunes: Turning on iTunes menus in Windows 8 and 7.

Restore it as explained here: iCloud: Restore your iOS device from iCloud.  This involves erasing your new phone, going back through the setup screens and when given the option, choosing Restore from iCloud Backup and follow the prompts.  You will be asked to choose the backup you want to restore to, and be shown a list of available backups.  Choose the backup of your old phone to restore to.

Be sure your new phone is connected to wifi and your charger while it is restoring the backup.

I don't know about those specific apps, but as a general rule, all your app data is restored when your restore an iCloud backup.  It is either restored by the backup itself, or synced back to your phone from iCloud if these apps store their data on the iCloud server.

As explained in iCloud: Restore your iOS device from iCloud:

Restore from an iCloud backup

1. On your iOS device, go to Settings > General > Software Update. If a newer version of iOS is available, follow the onscreen instructions to download and install it.You must update your device to the latest version of iOS to make sure you can restore from a recent backup of another device, such as a lost or broken device.
2. Make sure you have a recent backup to restore from.  Go to Settings > iCloud > Storage & Backup, then look at the bottom of the screen for the message Last Backup, followed by the date of the latest backup.For information about backing up manually now, see Back up your iOS device to iCloud.  If you don’t see a backup you expected to be there, see the Apple Support article iCloud: Troubleshooting restoring an iCloud backup.
3. Go to Settings > General > Reset, then tap “Erase all content and settings.”
4. In the Setup Assistant, proceed to “Set up your device,” tap Restore from a Backup, then sign in to iCloud.
5. Proceed to “Choose backup,” then choose from a list of available backups in iCloud.

You're welcome.