How can I recover deleted contacts and/or call history? Please help.

This matter sounds very important!
The only thing I can suggest is this;
Contact your cell phone carrier. Ask them to send you a itemized bill. This will probably have a small fee, but it will have a list of phone calls with the numbers that you made !
Make sure you request the monthly bill when you last called the number you seek!
And remember, in the future, write down all important numbers on a piece of paper or in a address book for future reference!
I hope this helps you!
Take care!

Bye the way!
Rooting your phone will not recover lost data. Rooting is mostly used to remove unwanted apps that your programming won't allow you to uninstall!
Just a heads up!

Usually, if the deleted contacts and/or call history is not overwritten by new data, you can use phone data recovery tool to help you recover them. Just use it to scan your phone, if the deleted contacts and/or call history can be scanned out, you can get it back easily.

Do you Know any proper way to root an Android Phone?

Neal
Proper way to root a phone.
Back up or record all your apps on external hard drive.
Install re-root program of your choice. There are many to choose from in play store and on the internet.
Then delete unwanted apps.
After check to see if there is any negative or unwanted effects to your device. If there are!
Then go to your back up and reinstall that app.
I have never done this myself, but that's the way to do it!

Have you turned on any built-in backup services? If no, try android recovery tool in the market. Actually I suggest backup your phone regularly.

You can call to your carrier and they can help you bring that back.

Before finding ways to restore or find back your contacts, you'd better to have a look at your Android device, because your contacts might not be deleted. So you need to make sure all your contats are being displayed.
1. Find "Contacts" and open it on your Android phone.
2. Tap on the menu button on the top right corner. Then choose "Settings" > "Contacts to Display".
3. Select "All Contacts". Now, you can return and check whether you got your contacts back or not.
If it is back, that means your contacts is not deleted but hidden. But if it is still not back, you can try the below method to get them back.

An excellent program is required for the task - MobiKin Doctor for Android (Win/Mac). It is easy to manage as you can recover lost, deleted, or formatted contacts on Android phones through only several clicks. Furthermore, before you make the recovery, the program allows you to preview all the contacts information, such as name, phone number, email address, company address and so on. So that you can choose what you want and restore them selectively. The restored contacts can be saved in the format of HTML or TXT.

— modified on Oct 25, 2018, 10:49:35 AM

The data recovery program only can recover the data that hasn't been overwritten.And the deleted data is easily overwritten by new files,as long as you add or create new files.So before recovering,you'd better to check if you deleted data still exsit on your internal storage.

Very sorry to hear the issue. To recover deleted contacts or call history, you can use a powerful data recovery tool like TunesKit iPhone Data Recovery. If you are using Android phone, there are similar tools. Just Google it.

You can use the third party app to find your deleted contact and call history on android, like KidsGuard Pro for Android, maybe you can have a try about this app.