Hello Murphythree,
Thanks for reaching out to the Apple Support Communities. We understand you are looking for some information on restoring Contacts and Notes back to your iPhone from iCloud. We are happy to help provide some guidance.
To start, do you know if you are syncing your Notes and Contacts in iCloud on your iPhone? If so, your iPhone would automatically be kept updated by the information stored in iCloud. You can check this by going to Settings > [your name] > iCloud and check to see if the switch next to Contacts and Notes are enabled there.
If they seem to be being removed automatically, we would want to check to see if your device has enough storage space available. Check to see your storage availability by going to Settings > General > iPhone Storage to see how much free space you have.
You can restore your iPhone from a previous backup from iCloud if a backup is available by following the steps listed in the article below:
Restore your iPhone, iPad, or iPod touch from a backup
Keep us updated on how it goes or if you have any questions!
Best Regards.